Performance and propeller load fluctuations of a ship in waves

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REPORT No. 163 S February 1972 (S 4/169, 214, 214a)

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

NETHERLANDS SHIP RESEARCH CENTRE TNO

SHIPBUILDING DEPARTMENT LEEGHWATERSTRAAT 5, DELFT

*

PERFORMANCE AND PROPELLER LOAD FLUCTUATIONS

OF A SHIP IN WAVES

(BEWEGINGEN EN SCHROEFBELASTINGSFLUCTUATIES VAN EEN SCHIP IN GOLVEN)

by

M. F. VAN SLUIJS (Netherlands Ship Model Basin)

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Het voortstiiwingsgedrag van schepen onder verschillende

zee-condities, afgezien van de vlakwaterconditie, verdient grote aandacht, hetgeen werd benadrukt gedurende de international

Towing Tank Conference in 1966.

Het totaal benodigd vermogen voor behouden vaart in zeegang kan worden gesplitst in het vermogen benodigd voor het over-winnen van dc weerstand in viak water, de gemiddelde yermo-genstoename als gevolg van golven en wind en een fluctuerend vermogen. De laatst genoemde component is vooral van belang voor de schroefwerking, waar ze de oorzaak kan zijn van

rende-mentsdaling, trillingen en cavitatie. Het onderhavige rapport beschrijft een onderzoek naar aard en oorzaak van genoemde vermogensfiuctuaties, waarbij gebruik werd gemaakt van de nog slechts schaarse ervaringen op dit terrein.

De invloed van de diverse parameters op de

vermogens-fluctuaties, zoals golfiengte, golflioogte, golfrichting, snelheid en diameter van de schroef is onderzocht op een scheeps-model met een blokcoëfficient van 0.825.

Op de interactie verschijnselen tussen schip en schroef en hun

invloed op de vermogensfiuctuaties is verder niet ingegaan.

Verder onderzock in deze richting is zeker de moeite waard. De resultaten van de proeven en de uitgevoerde berekeningen tonen aan, dat bet superpositie beginsel geldt voor de scheeps-bewegingen, vermogenstoenarne en fluctuaties van askoppel en

stuwkracht. De relatie tussen genoemde vcrschijnselen en de

golflioogte wordt in dit rapport nader toegelicht.

HaT NEDERLANDS SCHEEPSSTUDIECENTRtJM TNO

The propulsive performance of a ship in a variety of

circum-stances apart from the still water condition is something deserving

due attention, as was recognized by the International Towing

Tank Conference in 1966.

The total power required for sustained speed in a seaway can be divided into the power dealing with still water resistance, the mean power increase due to wind and waves and a power

fluctu-ation. The latter phenomenon is of particular importance with

regard to propeller action, where decrease of efficiency,

vibra-tions and cavitation problems are at issue. The present report is a first investigation into nature and origin of these power

fluctuations, making use of theory and results of experiments in this field, still being scarce.

The influence of several parameters on the power fluctuations, such as wave length, wave height, wave direction, ship speed and

propeller diameter, has been investigated, on a ship model of

0.825 block coefficient.

A detailed investigation into the interaction effects between

ship and screw and their influence on power fluctuations has been kept out of this study. These effects are certainly

worth-while to be investigated in future research.

The results of experiments and calculations, clearly show that the superposition principle holds with respect to ship motions,

power increase and fluctuations of torque and thrust. The

relation between these phenomena and the height of the waves encountered by the model is discussed.

THE NETHERLAND5 SHIP RESEARCH CENTRE

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page

List of symbols 6

Summary 7

I Introduction 7

2 Model test description 8

3 Considerations in presentation of results IO

3.1 Motion response characteristics 10

3.2 Powering response characteristics 10

3.3 Irregular wave characteristics Il

3.4 Scaling laws 12

4 Discussion of results 12

4.1 Motions in regular and irregular waves 12

4.2 Powering properties in regular and irregular waves 13

5 Conclusions 16

References 16

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LIST OF SYMBOLS

AG longitudinal centre of gravity forward of section 10 A_E expanded blade area

A0 propeller disc area projected blade area

B breadth

CB block coefficient

midship section coefficient

C,, prismatic coefficient

D propeller diameter

Fn Froude number = V/'.IgL

g gravitational acceleration GM metacentric height

J immersion of shaft

k wave number = 2/2

longitudinal radius of gyration centre of gravity above base

L length between perpendiculars N number of revolutions

N0 increase of revolutions in regular waves

o.7R propeller pitch at 0.7 radius Q0 amplitude of torque fluctuation

significant amplitude of torque fluctuation

Q mean torque increase in regular waves

mean torque increase in irregular waves amplitude of relative motion

significant amplitude of relative motion saw) wave spectral density

level trim draught

T.. natural period for heave T0 natural period for pitch

Ta amplitude of thrust fluctuation

Ta4 significant amplitude of thrust fluctuation

Tow mean thrust increase in regular waves

mean thrust increase in irregular waves

T mean wave period

V ship speed

Va amplitude of speed variation

Z number of propeller blades Z0 amplitude of heave

significant amplitude of heave

V displacement volume

heave-wave phase pitch-wave phase wave amplitude wave height =

significant wave height Oa amplitude of pitch

Oa4 significant anplitude of pitch

wave length, model scale mass density of water o. root-mean square value

w wave circular frequency =

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PERFORMANCE AND PROPELLER LOAD FLUCTUATIONS OF A SHIP IN WAVES

by

M. F. VAN SLUIJS

Summary

This report describes wave experiments with a cylindrical bow ship model of 0.825 block coefficient. Uni-directional head and following waves, regular as well as irregular, are considered.

During the experiments special attention has been given to the powering characteristics in waves, in particular with regard to fluc-tuations of torque and thrust, which are experienced by propellers designed for three different diameters by vortex theory.

For the purpose of measuring the torque and thrust fluctuations accurately, a water-lubricated shaft bearing system was utilized. For making the phenomena explicable, also measurements were made of the usual ship motions.

The results indicate that mean thrust, torque and revolutions increase of the propeller, vary with the squared wave amplitude. Motions and fluctuations of torque and thrust are linearly proportional to wave height.

Application of the superposition principle to motions, power increase and fluctuations is recognized to be valid.

I Introduction

Among the recommendations, made in 966 by the

11th international Towing Tank Conference to the

Seakeeping Committee, was a request to review the problem of determining the propulsive performance of a ship in waves.

To this purpose documentation was submitted by Todd [1] in 1970, from which it appears that at present mainly information is available about the mean power increase required for maintaining speed in a seaway.

Apart from a voluntary reduction of power, this mean increase arises from the combined effect of added resistance caused by wind and waves and a decreased propulsive efficiency.

Following Ochi [2], the total power required for a ship to maintain speed under realistic weather con-ditions is decomposed in the power determined by the calm water resistance, a mean power increase in waves and a power fluctuation. For the latter phenomenon the ship motions may be the predominant factor.

A summary of the effect of wave action upon the ship and its propulsive system, in which interaction between the various quantities is not taken into ac-count, is given in figure 1.

Few data are as yet known about fluctuations or variations, which are experienced by the ship propeller in every cycle of wave encounter. So far, this aspect has been investigated as a sub-problem only, by a few authors, see e.g. Ochi [2], Gerritsma [3] and Yama-nouchi and Ando [4].

Knowledge of the fluctuations is, however, deemed of essential importance in order to enable the

assess-ment of upper and lower limits, within which the propeller is desired to work efficiently.

When fluctuations become too large, efficiency will decrease. Moreover, large fluctuations may become

detrimental because of their inducing propeller vibra-tion and'cavitavibra-tion.

For above reasons the behaviour and powering

characteristics in waves of a ship model with a block coefficient of 0.825, were investigated in the Sea-keeping Laboratory of the Netherlands Ship Model

Basin [5].

As already extensive investigations into the merits of cylindrical bows in calm water were conducted at the N.S.M.B. by Muntjewerf [6], a hull form could be selected for the present wave experiments which

ap-WAVES CALM WATER POWER SHIP MOTIONS SCREW CHARACTERISTICS MAX POWER DESIRED POWER SUSTAINED SPEED RESISTANCE INCREASE THRUST AND TORQUE FLUCTUATIONS CAVITATION SCREW RACING SLAMMING WATER SHIPMENT CARGO SHIFTING

1

INTERVENTION' ---I BY MASTER

Fig. 1. Effect of waves upon the ship and her propulsion.

WAKE THRUST DEDUCTION

THRUST AND TORQUE INCREASE

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8

peared to have the optimum calm water performance. This report outlines the results of the relevant

re-search

in waves and deals in particular with the

propulsion characteristics of the single-screw cylin-drical bow vessel, successively equipped with three screws of different diameters.

2 Model test description

The experiments were performed in the Seakeeping Basin having a water depth of 2.5 metres.

A wooden ship model with a length of about 4

metres was employed for the wave tests. Its shape corresponds to that of model no. 2991 B from reference [6], which is the basic ship form fitted with an optimum cylindrical bow for calm water. The model scale is

1 60.

Principal particulars are listed in Table I, whereas the lines and profile are being shown in figure 2.

The tests were conducted within a speed range of

0.12< <0.17,

/gL

while the model was successively equipped with a

singel-screw, designed according to the vortex theory for 90, lOO or 110 revolutions per minute for the full size ship.

Their main characteristics are given in Table II and are illustrated in the figures 3 through 5.

During the tests in waves the model was free in its

vertical and longitudinal movements; rolling and

lateral motions were prevented by two guides so as to keep a constant heading.

The model was propelled at model self-propulsion point. No friction correction for model-ship resistance scale effect was applied; a procedure which is in

agree-denomination

length between perpendiculars breadth

draught level trim displacement vohime

block coefficient prismatic coefficient midship section coefficient

centre of buoyancy forward of section 10

centre of gravity above base

metacentric height natural heave period natural pitch period

longitudinal radius of gyration centre line shaft below water

level

Fig. 2. Profile and body plan of 0.825 block coefficient ship.

5 14 10

ment with the recommendations of the International Towing Tank Conference 1960.

For the test set-up the model was connected by a light-weight push rod in the centre of gravity to a low-mass and low-friction subcarriage, so that no appreci-able forces were introduced.

Throughout the experiments the following quantities were simultaneously recorded:

- Pitch angles, determined by a gyroscope

- Heave at the centre of gravity, sensed by a vertical push rod driving a potentiometer

- Surge (for phase determination), measured by the horizontal excursion of the subcarriage

- Relative motions forward and aft along the stem and stern respectively, sensed by wave probes

Thrust, torque and their fluctuations, obtained by a strain gauge dynamometer

RPM and model speed, measured by slotted disks with photo-cell pick-up

- Waves, sensed by a capacitance type probe.

Table I. Model and ship specifications

sym-bol twit model st il)

L m 4.0445 242.67 B m 0.6222 37.33 TM m 0.2348 14.09 V m3 0.4875 105,306 CB

-

0.825 0.825 Cp 0.830 0.830 CM 0.994 0.994 AG m 0.0853 5.12 KG m 0.1700 0.20 GM m 0.0932 5.58 T, sec 1.30 0.1 T,, k,,,, sec %L 1.18 24 9.1 4 I m 0.15 9.0

/

FP

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1.0 R 0.85 R 09 R 088 a7R 06 R 0.4 R

Table 11. Propeller model specifications

propeller propeller propeller

denomination symbol unit no. 4201 no. 4202 no. 4203

Fig. 3. Vortex theory propeller no. 4201.

-85.90 85.67 84.Z3 83.28 81.50 79.42 77.08 \- 74.55 i.t98

Since reliable information was to be gathered about powering fluctuations, special attention was paid to the power measuring instrumentation and equipment. lt was realized prior to the tests, that a conventional shaft bearing system, in combination with mechanical

couplings, was not appropriate due to its intrinsic

vibration and disalignment problems.

Therefore a special water-lubricated shaft support was designed, the principle of which is shown in figure 6. lt enabled the measurement of thrust and torque without the use of electronic filters.

The propelling mechanism was electronically con-trolled such that the number of revolutions was kept constant throughout.

Shaft and screw were scaled to model size also as

PROPELLER NO 4202 D .133,,, PO,,!0 .0564 z

.4

A0f5 .0554 A../9 . 0.516 PROPELLER No 4203 D 1250mm Po/0 . 0,656 z . 4 Ao/A 0593 AJA 0.548

regards weight; it was accomplished that the natural frequencies in water of the system consisting of shaft, screw and the spring of the thrust transducer were

about 60 cps, which is well above the maximum fre-quency of wave encounter.

The weight distribution in the model was adjusted on a special low-mass trimming table, by means of which the correct position of the centre of gravity in the vertical and horizontal directions was obtained.

The longitudinal radius of gyration was adjusted by measuring the periods of oscillation when the model was placed upon this table in such a way that its centre of gravity coincided with the pivoting axis.

The testing programme consisted of self-propulsion experiments in regular and irregular waves for the

head and following sea direction, during which the

following aspects on the behaviour and propulsion were considered:

- Effect of wave length - Effect of wave height - Effect of wave direction

- Effect of regularity and irregularity of waves - Effect of screw diameter

- Effect of forward ship speed.

5 R 9845 .. 0.9 R Q.ß R _____________ 9813 97.15

__________________

R

Rtl

95,60 0.6 R 93.68 0.5 R 91 37

-0.4 R 88.75 0.3 R 85.97 R 83.03

...

t

-0,95 R 91,22

It'

093 07 R 98,53

I

86.62 Q5 R 84,33 Q.4 z .7 03 R

&ÎI

_

L4L. 0,2 R

-

-4

t

...

l4l.7 l33.3 ¡25.0 0.675 0.664 0.666 0.530 0.564 0.593 4 4 4 10 R 9858 1.0 R 9138 propeller diam. D mm pitch ratio P,,7R/D -expanded blade

area ratio AE/AO

-numberof blades Z

-W rection of rotation right-handed

PROPELLER No 4201 D - 141.7 rEm 0.675

.4

0530 -0460

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lo

/

7HT

/

WATER IN LE T

3 Considerations in presentation of results 3.1 Motion response characteristics

Pitch, heave, relative motions amplitudes and speed variation derived from the regular wave tests are shown in a dimensionless form versus the wave length - ship length ratio )]L. Pitch has been non-dimensionalized through dividing its amplitude by the maximum wave

slope.

Accordingly heave and relative motions amplitudes are given, divided by the wave amplitude. This under the assumption that motions vary linearly proportional to wave height, which appears at present also to be true within, evidently, practical limits of measuring accuracy.

Forward speed variation is non-dimensionalized by dividing its amplitude by the wave frequency multi-plied by the wave amplitude.

Phase angles are defined as the lag of the wave at the centre of gravity of the model with respect to the motion amplitudes:

Fig. 6. Set-up of power measuring instrumentation.

THRUST arid TORQUE TRANSDUCER

mean resistance of a ship in waves arises from the

interaction of the harmonic wave forces and the

har-monic ship motions, resulting in a net resistance force when wave and motion are out of phase. The

mean resistance increase in waves can be written as:

Raw = k(2aFz 5ifl E:F+OaMO S1'ehM)

where

k = wave number Za = heave amplitude

Lia pitch amplitude

F0 = wave exciting force amplitude M0 = wave exciting moment amplitude

= phase between heave and wave exciting

force

= phase between pitch and wave exciting moment

From the above formula it follows that the mean in-crease of resistance due to waves varies as the squared

wave amplitude .

Various systematic resistance experiments in waves

were carried out by, for instance, Sibul

[8] and

Nakamura and Shintani [9], from which a

satis-factory agreement with theory was found.

Transforming mean resistance increase into thrust or torque increase, see reference [3], shows that pro-peller action is only affected to a minor degree by the cyclic load variations due to waves.

Henceforth the present test results as regards mean thrust and torque increase are non-dimensionalized by dividing these quantities by the squared wave

am-plitude in combination with the ship and propeller parameters:

II TO DRIVING MOTOR

t to t ti TIMEt

3.2 Powering response characteristics

According to Havelock [7] the major part of added

COUPLING

WATER FILM

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NawD3LV

Mean increase of revolutions =

gB2

Mean thrust increase

-

QgB2 T00,L

Q,L

Mean torque increase

QgB2D

The effect of waves upon fluctuations of thrust and torque in every cycle of wave encounter will be con-sidered from a point of view of a free-running non-oscillating propeller.

From open-water experiments, conducted by Mc-Carthy et al. [10] and Taniguchi and Tamura [li] in regular waves, local advance coefficients were deter-mined by calculating the mean orbital velocities of the waves in way of the propeller disc.

The thrust and torque coefficients for the propeller when operating below wave crests and wave troughs were plotted against their local advance coefficients, and the results were found to be in good agreement with the open-water characteristic curves fort he pro-peller in uniform flow.

Since these experiments were done in waves with varying lengths and heights, it implies that thrust and torque fluctuations of a free-running propeller in waves vary proportionally with wave height, provided that the propeller is sufficiently submerged.

When the propeller oscillates horizontally and ver-tically, perturbation velocities are induced.

The effect of vertical perturbation velocity is, how-ever, small as has been found by Taniguchi et al. [12]. For a propeller working in the behind-position inter-action effects between ship and screw will arise more-over. These phenomena are, however, not fully expli-cable as yet, since both theory and experimental results are absent in this respect.

Gerritsma [3] supposed that fluctuations originate mainly from variation of horizontal flow in the pro-peller, caused by the orbital wave motion and surging of the ship, a supposition which is in support of the

linear relationship between power fluctuations and wave height.

The present experimental data seem to confirm

that linearity with wave height is justified within the experimental range of accuracy.

In the presentation the following dimensionless

notation has therefore been employed:

Thrust fluctuation

QgB2

Torque fluctuation Q0

3.3 Irregular wave characteristics

All information derived from the irregular wave model tests has been transformed into data that apply to the full size vessel.

In the presentation of the results, the sea condition is indicated by the Beaufort number, which actually indicates wind speed.

Since there is no direct relation between wind speed and the state of the sea, this presentation is conse-quently not completely correct.

However, the procedure is often adopted since it is easier to estimate wind speed than to describe the state of the sea.

As to the relation between wind and waves the data of Roll [13] were used, which are based upon observa-tions made on board North Atlantic weatherships.

For present purposes a wind Beaufort 8 sea was considered, having an average observed wave height of 4.85 metres and an average observed period of 8.4 seconds.

The character of this sea condition is further em-bodied by its power spectrum, which is represented by the formula:

AB

s(w) = e w4

Apart from the values of A and B this formula depicts spectra similar in shape to the Pierson-Moskowitz [14] formulation for fully developed seas.

When the wave energy spectrum is related to actual observations at sea, it is generally assumed that the average observed wave height conforms to the cal-culated mean of the one-third highest waves(= signifi-cant wave height) and that the observed period of the waves corresponds to the calculated mean period.

In accordance with the recommendations made in reference [15] the mean wave period is based upon the first moment of the power spectrum. Thus for a

narrow-banded spectrum it follows that:

Observed wave height = ₌ J s(w) dw

O

5s(co) dw Observed wave period = T = 2ir O

Jas(adw

Thence the coefficients A and B are related to signifi-cant wave height and mean wave period following:

A = 0.25

_(Ç)2

/

_2ir4

B = t 0.817---T

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12

The spectrum as formulated above is illustrated by

figure 21 of the appendix in comparison with that

produced in the basin. The distribution of the instan-taneous wave elevations is also indicated, which shows a good agreement with the normal Gaussian prob-ability.

3.4 Scaling laws

The accepted basis of predicting motions and powering in waves of the full size ship from that of a model, rests on the assumption that basically Froude's law of simil-itude is to be fulfilled.

Effects of viscosity are negligible when head and following waves are considered since experimental results check generally well with potential theory cal-culations. In particular this holds true as far as motions of ships are concerned.

A full description of the scaling law applicable to the test results is given in Table III.

4 Discussion of results

4.1 Motions in regular and irregular waves

As most of the dynamic quantities measured, were dependent on the same parameters, i.e. the wave length and the forward ship speed, a standard form of pre-sentation was chosen for ship motion quantities. The results of the tests in regular waves are given in the figures 7 through 13 of the appendix.

From literature, as for instance Saunders [16] and Tasaki [17], it is known that the damping effect of the rotating screw upon ship motions is insignificantly small. The present experiments showed that motions

are not affected by the application of screws with

different diameter. Therefore only one set of motion response curves is presented.

All motion response curves exhibit the usual

ten-dencies and show a good linearity with wave height, which was not expected as to relative motions.

Phase angles of pitch and heave are given only for the wave height ratio of 1/70, because of their inde-pendence of wave height. They could solely be deter-mined with reliable accuracy for the head sea condition. Since during the experiments in head seas pitch and heave in combination with their phase relationship to the waves were determinable, the measured relative

motions forward and aft could be related to these

quantities according to the following formula:

()2+x2()2+1

_2x?-

cos(cs0,.)--z o

-2 ¿!- cos ( - kx) + 2x cos (c kx)

where

s» relative motion amplitude

ça = wave amplitude = heave amplitude

X = longitudinal distance from the centre of

gravity to location under consideration ou = pitch amplitude

C- = heave phase pitch phase

k = wave number = 27r/Ä = wave length

The corresponding co-ordinate system is right-handed and fixed to the ship, i.e. positive x is forwards, positive z is upwards and positive O is bow down.

Results of these calculations are given non-dimen-sionally in Table iV, so that they are directly

com-parable with the values of the figures 11 and 12 of the appendix.

Table III. Scaling laws

symbol

quantity model ship relationship non-dimensional value

speed Vm VS = 1J2. y v L

speed variation Varn Van Van = A'/' Vam Val 0)

length Lm L5 L5 =ALrn mass Mm M5 M,, 3Mm frequency heave Zam (02, Zap (O = AIJ2.

Zap = Zam Zala

pitch Oap = 0am Oa/kCa

relative motion _5am Sap 5ap = Sam SaIa

thrust increase Taw,a Tawp Tawp = 3Tawm Tam L/gB'2

thrust fluctuation Tam Tap Tap = )3Tam TalQgB2a

torque increase

torque fluctuation Qawm_Qam QawpQap

Q awn = 4Qawm

f)

_QaIgB'a2

Qaw /)gBS12

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Table 1V. Calculated relative motions from pitch and heave in regular head waves uncorrected and corrected according to Tasai _[18]

As regards these calculated relative motion responses, two sets of data are presented.

The first column of Table IV shows the relative

motions when the wave surface is assumed not to be disturbed.

in the second column the disturbance of the wave surface due to the oscillations of the ship is accounted for, the degree of which has been estimated according to Tasai [18].

Though this correction method may be arbitrary to some extent, it follows that by applying this a better agreement between calculated and measured relative motion at the stem is obtained.

For the relative motion at the stern, the corrected

data points deviate substantially from both the un-corrected values and the experimental results. This implies that the disturbance of the waves, when passing along the ship, is not completely accounted for when using Tasai's method.

In order to have more information in this respect, additional tests should be conducted with a restrained model for establishing wave deformation. Moreover, waves transmitted by the oscillating ship should also be measured for gathering full knowledge of the phe-nomenon.

For the calculation of the behaviour of the vessel in irregular seas, based upon the results of tests in regular waves, methods are used which are treated by various

authors of handbooks on the behaviour of a ship at sea, see e.g. Vossers [19].

TableV. Comparison between calculated and directly measured motions for Beaufort 8 seas. (Significant double amplitudes)

Irregular ship motions in the vertical plane are pre-dicted for the full scale ship using its model responses to the regular wave height ratio of 1/70 and assuming that the response to individual regular wave compo-nents can be linearly superimposed.

For the purpose of the calculation the wave spectrum indicated by the full line in figure 21 was employed, of which the significant wave height is 4.75 metres and the mean period 9.6 seconds.

This spectrum represents the spectral density pro-duced in the basin obtained by frequency modulation of the wave generator.

The model experiments in irregular seas were run during a time period corresponding to 30 minutes for the full scale, being sufficiently long in view ofa reliable statistical treatment.

One-third highest values were determined which are given in Table V, in comparison to those calculated from. the regular wave experiments. They apply to the

full size vessel.

A good correlation between calculated and directly measured values is resulting.

4.2 Powering properties in regular and irregular

waves

Mean thrust and torque increase and that of revolu-tions in regular waves was assessed by subtracting the thrust, torque or revolutions for the model in calm water from that recorded in waves for the same speed. The dimensionless quantities are given for the

pro-aI4a forward (uncorrected) a/a aft (uncorrected) aIa forward (corrected) Sa/ aft (corrected)

Fn 0.120 Fn 0.145 Fn 0.170 Fn 0.120 Fn 0.145 Fn 0.170 Fn 0.120 Fn 0.145 Fn 0.170 Fn 0.120 Fn 0.145 Fn 0.170 0.6 1.26 1.17

Ill

0.95 0.99 1.00 1.18 1.12 1.10 1.18 0.89 0.91 0.8 1.83 1.51 1.36 1.16 0.90 0.80 1.63 1.36 1.24 1.38 1.08 0.97 0.9 2.51 2.43 2.25 ¡.45 1.12 0.85 3.18 2.16 2.02 1.71 1.33 1.02 l.0 3.07 3.00 2.93 1.77 1.58 1.49 3.94 3.80 2.59 2.06 1.86 1.76 LI 3.10 3.13 3.15 1.62 1.69 1.74 3.83 3.90 3.96 1.87 1.97 2.04 1.2 2.83 2.95 3.03 1.65 1.68 1.76 3.44 3.63 3.77 1.89 1.94 2.04 1.3 2.55 2.76 2.92 1.66 1.59 1.57 3.07 3.36 3.58 1.88 1.82 1.80 1.5 1.88 2.12 2.30 1.64 1.58 1.52 2.23 2.53 2.77 1.84 1.78 1.73 wave

2a

(m) 2O (degr)

2.

forward (m) 2aaft (m)

speed(kn) direction measured calculated measured calculated measured calculated measured calculated

10.5 head 1.38 1.42 2.02 2.09 0.47 11.10 4.24 4.36 13.3 1.47 1.51 1.94 2.03 10.64 10.57 3.70 3.93 17.1 .49 1.58 1.99 1.97 9.41 10.40 3.23 3.45 11.2 following 0.85 0.72 1.23 1.25 3.91 3.78 3.89 3.85 14.3 0.77 0.72 1.19 1.24 3.87 3.63 2.94 3.20 16.3 0.78 0.76 1.20 1.21 3.58 3.44 2.72 3.06

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14

Table VI. Non-dimensional power components in head waves (Fn = 0.145)

Tau. L

gB22 gB2

Ta

>< 10-e

peller model 4202 in the subjoint figures and can be used for predicting the behaviour of the full size ship in similar conditions.

Results for the propeller models 4201 and 4203 are tabulated in Table VI and VII.

It is shown that for the range of variables considered in the tests the mean increases of thrust, torque and

revolutions are approximately proportional to the

squared wave amplitude at constant speed and con-stant wave length.

The character of mean thrust, torque and revolu-tions increase agrees well with that of the combined heave and pitch motion.

The amount of increase is highest when the

syn-Q,,,,, L

9gB2D2

Table VII. Non-dimensional power components in following waves (Fn = 0.170)

9gBD Qa _xlO_ N D3LVow gBa2 0.4 1/70 2.7 2.7 5.6 5.5 0.27 0.22 3.6 4.6 0.90 0.80 0.6 3.0 3.0 6.6 6.6 0.29 0.23 5.4 6.3 1.80 1.46 0.8 2.5 2.3 6.4 6.6 0.27 0.22 6.2 7.0 0.90 0.63 0.9 1.6 1.7 6.8 7.2 0.19 0.13 6.3 7.6 1.20 1.28 1.0 1.5 1.6 7.0 8.6 0.20 0.14 7.0 8.1 1.50 1.30 1.2 1.7 1.4 9.0 9.8 0.19 0.13 7.4 8.6 1.10 0.96 1.5 1.6 1.8 8.2 8.2 0.15 0.10 5.2 6.9 0.90 0.42 0.9 1/100 1.5 1.7 6.0 6.7 0.19 0.16 6.3 7.1 1.40 1.01 1.0 1.9 1.6 7.2 8.2 0.19 0.15 7.0 7.8 1.60 1.01 1.2 1.8 1.8 9.0 9.2 0.18 0.15 7.4 8.3 1.50 0.65 0.9 1/50 1.3 1.8 7.1 7.7 0.17 0.14 6.5 8.0 1.64 1.00 1.0 1.5 1.4 8.5 9.2 0.19 0.15 7.6 8.4 1.90 1.10 1.2 1.7 1.3 9.8 10.3 0.17 0.14 8.1 8.8 1.31 0.74

chronous motion appears in waves having a length al-most equal to the ship length.

The rate of change of thrust and torque increase with respect to forward speed is small.

Mean thrust increase is not influenced by the dif-ference in propeller characteristics; torque increase

will become, of course higher in case the propeller diameter is larger.

Torque and thrust fluctuations are approximately linear with wave height.

When the present results are compared with those reported before by Gerritsma [3] it will be seen that

the results of Gerritsma are somewhat higher.

In this respect it should be remembered that these

L Ta

>

egB2a

propeller no. propeller no.

)./L /L 4201 4203 4201 4203 0.4 1/70 2.5 2.4 5.1 5.6 0.6 3.2 3.6 5.4 6.0 0.8 4.3 4.6 6.4 6.8 0.9 6.8 7.1 7.7 9.2 1.0 7.8 8.3 14.0 13.5 7.2 7.1 13.5 14.3 1.2 5.0 5.3 12.3 13.3 1.3 3.6 3.0 10.9 11.9 1.5 0.9 0.6 8.0 9.0 0.9 1/100 6.6 6.3 8.1 8.6 1.0 8.0 7.8 13.3 12.8 1.1 7.4 7.7 13.4 14.0 1.2 5.6 6.2 12.5 12.9 0.9 1/50 6.3 6.1 7.8 9.0 1.0 8.1 8.3 12.6 13.7 1.1 7.1 7.7 13.9 14.8 1.2 4.7 5.0 12.8 13.7

propeller no. propeller no. propeller no. propeller no. propeller no.

¿IL /L 4201 4203 4201 4203 4201 4203 4201 4203 4201 4203

9YB2Da2 Q au,

ogB2Da gB22

Qa _{< l0-} NaWD'LV

propeller no. propeller no. propeller no.

4201 4203 4201 4203 4201 4203 0.34 0.32 3.8 4.5 2.5 2.0 0.41 0.38 4.4 5.0 3.0 2.6 0.58 0.53 5.2 6.2 5.5 4.0 0.73 0.65 6.3 8.2 8.3 6.5 0.93 0.83 9.3 11.0 9.2 7.6 0.97 0.84 10.9 11.6 8.8 5.8 0.68 0.45 9.4 10.4 6.6 4.4 0.41 0.26 7.8 9.0 4.4 3.5 0.20 0.11 5.1 6.2 1.5 0.5 0.76 0.66 5.7 7.9 8.0 6.3 0.95 0.85 8.6 10.4 9.8 7.4 1.00 0.86 10.6 11.0 8.1 6.3 0.71 0.46 9.0 10.0 6.3 4.9 0.71 0.63 6.6 8.5 8.4 6.3 0.90 0.80 9.8 11.3 9.5 7.4 0.95 0.81 11.2 12.0 7.6 5.2 0.65 0.43 9.8 10.8 5.8 4.6

(14)

differences may originate for the major part from

dif-ferences in block coefficient and propeller charac-teristics.

Though the regular wave heights were chosen in such a way that the screws were completely submerged throughout the tests, fluctuations are found largest for the smallest diameter of propeller. This fact is contrary to what would be expected since a larger diameter propeller will be more sensitive to air drawing, though not observed during the experiments, than a smaller one and hence introduce larger fluctuations.

A possible explanation for this phenomenon can nevertheless be derived from the unsteady airfoil

theory when it is assumed that the surge motion is the reason for this difference, when the average wake is assumed to be constant and when the gust velocity is the same for the three propellers.

According to the two-dimensional airfoil theory, the fluctuating lift force L per unit length in span-wise direction is given by:

L= 7rQCUH(wr)

where

= mass density of water

c = chord length

U = resultant entrance velocity = gust velocity

H((Úr) = dynamic response of profile Wr = reduced frequency = 27r(c/A)

= wave length Also holds

T= Lcosß

and 2rrNR07 2irNR07

cosß=

= U \/V+47r2N2R7 where:

R = radius of blade section under consideration (in subject case R07)

N = number of revolutions = speed fluctuation

Then the thrust fluctuation becomes: 4,r2N2R7 T = constantS V

,JV2+4r2N2R2

in which V0 is the same for the three propellers. Hence it follows that the largest thrust fluctuations will be found for the propeller of which N R007 is lar-gest, which is propeller no. 4203 having the smallest diameter.

Thus thrust fluctuations are controlled by the hydro-dynamic pitch angle of the screw.

Figures 19 and 20 show that thrust and torque fluc-tuations can become large as compared to the mean increase, in particular when the ship navigates in waves approaching from the stern.

Results of the thrust and torque measurements in irregular seas have been plotted in the figures 22 through 31 for the full size ship.

The thrust (or torque) of a ship moving at a constant RPM in irregular waves increases by a certain magni-tude (T,,) over that required to move the ship in calm water, and in addition, oscillates (Ta) with wave fre-quencies about its mean increased value.

[n this case, T0 is a consistent value, the magnitude of which is a function of wave height and period and ship speed.

Thrust fluctuation T0 varies at random as is illus-trated; its statistical distribution corresponds to the normal Gaussian probability law.

The width of each column of the histograms as given in figures 22 through 31 is equal to Jvariance of the recorded signal.

In the figures 32 through 35 information of thrust and torque for propeller 4202 is given as a function of

ship speed.

Dashed lines indicate values which were directly

measured in the irregular Beaufort 8 sea; the solid circles apply to calculations from the regular wave test

results.

H(Wr) can be considered as constant; the fi uctuating lift force can then be expressed as:

L = constant U

with

(15)

16

The mean thrust increases and fluctuations in

irre-gular waves were determined from the reirre-gular wave responses in combination with the superposition

prin-ciple.

Mean thrust increase has been derived with:

Taw 2gB2

(

aw

) s(we) dw L o QgB

The significant value of the amplitude of thrust fluctua-tion has been determined from:

= 2QgB2

( T

\2

$ t

_{o \QgBJ}

, I S(W,)dW

Similar expressions are valid for the other propulsive quantities.

lt follows that for the speed range under considera-tion the agreement between the directly measured

values and the predicted values is very good. The validity of the principle of superposition seems to be proved, both as regards thrust and torque in-crease and fluctuations of thrust and torque in the case that the engine is operated at constant revolutions.

5 Conclusions

Experiments carried out with a ship model of 0.825 block coefficient in a wide range of wave lengths and heights have shown that, in as far as regular head and following waves are considered, motions vary linearly proportional to the wave height.

Maximum increase of powering characteristics does not necessarily coincide with maximum amplitudes of motion.

Mean thrust, torque and revolutions increase, re-quired to maintain speed in a seaway, can be assumed to be proportional to the square of the wave height, whereas fluctuations are found to vary proportionally to wave height, when the propeller turns at constant revolutions.

Application of screws, differing in diameter, results in an almost constant mean thrust increase; mean torque increase is larger when the propeller turns more

slowly.

Fluctuations of thrust and torque are larger in case the propeller diameter is smaller, provided that the tips are completely submerged.

It has been demonstrated that the linear

superposi-tion principle is valid both with respect to mosuperposi-tions

and power increase and to the fluctuations of thrust

and torque, which are experienced by the screw in every cycle of wave encounter.

Though the most important conclusions are

men-tioned, a detailed study of the results will yield even more information. lt may, moreover, lead to further research into the problem of propulsion of a ship in waves to provide an experimental basis for the predic-tion of cavitapredic-tion, air drawing and screw racing.

References

F. H. TODD. Ship power prediction in waves. 12th Inter-national Towing Tank Conference, Seakeeping Committee, Appendix VI, Rome, 1970.

M. K. OCHs, Statistical properties of powering

characteris-tics in waves. 15th American Towing Tank Conference,

Ottawa, 1968.

J. GERRITSMA, Propulsive performance in waves. Notes of

4th Bi-annual seminar Ship behaviour at sea, Stevens

Institute of Technology, January 1963.

Y. YAMANOUCHI and S. ANDO, Experiments on a Series 60, CB 0.70 ship model in oblique regular waves. Ship

Research Institute, Tokyo, No. 18, October 1966.

W. P. A. VAN LAMMEREN and G. VOSSERS, The Seakeeping

Laboratory of the Netherlands Ship Model Basin.

Inter-national Shipbuilding Progress, Vol. 4. 1957.

J. J. MUNTJEWERF, Methodical series experiments on

cylindrical bows. Transactions of the Royal Institution of

Naval Architects, London, Vol. 112, No. 2, April 1970.

T. H. HAVELOCK, The drifting force ori a ship among waves.

Philosophical Magazine, B 23, Series 7, 1942.

O. J. SIBuL, Increase of ship resistance in waves. College of Engineering, University of California, Report No. NA-67-2,

1967.

S. NAKAMURA and A. SHINTANI, Propulsive performance of

a Series 60, CB = 0.70 ship model in regular head waves. 12th International Towing Tank Conference, Subject - Sea-keeping, Rome, 1970.

J. H. MCCARTHY, W. H. NORLEY and G. L. OBER, The

per-formance of a fully submerged propeller in regular waves.

David Taylor Model Basin. Report 1440, Washington,

May 1961.

Il. K. TANIGUCHI and K. TAMURA, Propeller open tests in

waves. Mitsubishi Experimental Tank, Report No. 221.

Tokyo, April 1955.

K. TANIGUCHI, H. TANIBAYASHI and N. CHIBA, Investigation

into the propeller cavitation in oblique flow. Report no. 2221 of the Experimental Tank Laboratory Mitsubishi

Heavy Industries Ltd. May 1966.

H. U. ROLL, Die Grösse der Meereswellen in Abhängigkeit von der Windstärke. Deutscher Wetterdienst, Seewetteramt. Hamburg 1954.

W. J. PIERSON and L. MosKowrrz, A proposed spectral form for fully developed wind seas based on similarity theory

of S. A. Kitagarodskii. Journal of Geophysical Research,

Vol. 69, December 1964.

Proceedings of the international Ship Structures Congress,

20-24 July 1964. Report of Committee No. 1 on

environ-mental conditions.

H. E. SAUNDERS, Hydrodynamics in ship design. Society of

Naval Architects and Marine Engineers, Vol. III, 1965. R. TASAKI, On the characteristics of the driving machine in the self-propulsion test among waves. Society of Naval Architects of Japan, Vol. lOI, August 1957.

F. TASAI, Wave height at the side of two-dimensional body oscillating on the surface of a fluid. Report of the Research Institute of Applied Mechanics, Kyushu University, Vol. IX,

No. 35, 1961.

G. VOSSERS, Fundamentals of the behaviour of ships in

waves. International Shipbuilding Progress, 1959, 1960,

(16)

(17)

IS

Fig. 8. Heave - wave phase.

15 lo 05 .200 -100 X L o o X L lOO L 50 Fn 0.170 HEAD WAVES FOLLOWING WAVES

L

t L lOO -_j_. L -70 L 50 Fn :0.145 HEAD FOLLOWING WAVES L t

HFn

:0.120 HEAD WAVES FOLLOWING WAVES

L

t L -70 En r 0.145 HEAD WAVES . I Fn:0170 WAVE S .200 w .100 Ai O o -100 o OS 10 À L

Fig. 7. Heave response.

L 70 Fn 0.120 HEAD WAVES 05 to 05 10 LS 05 10 15 X L Os lo 15 05 10 S lo

4i'

05 .200 .100 a -lOO Io IIj 05 o

(18)

O o O

-200

05

Fig. lO.

Pitch - wave phase.

loo -200 o-5 X L lOO 200 7 05 HEAD WAVES Fn 0170 _.-_ ---L -100 L 70 1 L -50 Fn 0120 HEAD WAVES

___ir

FOLLOWING WAVES L L 100 L 70

L

i L -50 Fn 0145 HEAD WAVES FOLLOWING WAVES

-L

1 L lOO L 70 L 50 Fn 0.170 HEAD WAVES FOLLOWING WAVES L -70 Fn O 120 AVES X X X L L Fig. 9. Pitch response. lo 05 10 15 05 10 10 15 05 10 ₀₅ 10 OjU 0.5 10 OS o

(19)

L

Fig. 11.

Response of relative motion at the stem.

O 4 u. 4 o 4 o k Ç 70 L 50 FnrO.145 HEAD WAVES FOLLOWING WAVES L 100 -._ L 70 Ç Fn r 0.170

FOLLOWING WAVES

/Y4

L 100 L -70 Ç I L -SO n r 0120 HEAD WAVES WING WAVES 05 IO IS o 10 IS 05 10 15 o

_4.;

(20)

05

Fig. 13.

Response of speed variation.

o 3 o ₀₆ ₀₄ o X L lOO I

L7

L

i Fn0120 HEAD WAVE FOLLOWING WAVES çW I L -100 -..-_!_ L 70 L -50 Fn 0.145 HEAD WAVES FOLLOWING WAVES L -L 100 _ L 7Ö L 50 HEAD WAVES

LOW ING WAVES

L 100 L 70 L 50 Fn O 120 HEAD WAVES 'FOLOWING WAVES çW L -100 .... -_L. L -70 L -50 FnO.145

I

HEAD WAVES

rr

FOLLOWING WAVES L -100 -.---V .i_ L 70 L -SO Fn 0.170

____.aillíl

r

HEAD WAVES

AÀ

.FOLLOWING

X A A L 05 IO 15 X L Fig. 12.

Response of relative motion at the stern.

05 lo 15 A L 05 05 10 10 l5 05 10 06 04 > 3 02 3 02

(21)

Fig. 14. Mean increase of revolutions of propeller 4202.

05

Fig. 15. Mean increase of thrust of propeller 4202.

Is lo 5 o A

_

L

I L lOO _{_L} L 70

L

i L 50 Fn 0120 HEAD WAVES FOLLOWING WAVES L __ 1:i -i 100 Fn 0.170 HEAD WAVES FOLLOWING WAVES L L -100 I L 70 L L -50 Fnr0145 HEAD WAVES FOLLOWING WAVES L I tiFn 0120 HEAD WAVES FOLLOWING WAVES L i L 100 L 70

L

i L -50 Fn 0.170 HEAD WAVES FOLLOWING WAVES L L lOO L 70

L

L -50 Fn r 0 145 HEAD WAVES FOLLOWING WAVES X X X L L L lo 15 05 IO 15 05 lo IS 05 10 15 10 05 10 15 15 lo o o o 05 o 15 o z 5 ₁₅ ₁₀ 5

(22)

S _o

15 _Io

a LE

05

Fig. 16.

Thrust fluctuation of propeller 4202.

00 05 IO IS X w IS o lO l0 5 l0 o o L 1 L 100 . L 70

L

L -50 1 FnO.12O -HEAD WAVES FLL0W ING WAVES L L 1 L 100 1 L 70 L 50 Fn C17: L L HEAD WAVES FOLLOWING L L 100 L 1

L

i FnQ.145 HEAD WAVES FOLLOWING WAVES

L

L L -loo -_L. L 70

L

1 L -50 Fn :0120

___HEAD

W4

FOLLOWING WAVES L

L

L 100 L 70

L

i L -50 Fn :0145 HEAD WAVES FOLLOWING WAVES

L

t L L lOO -L. L 70

L

L -SO Fn0170 ADwAVE5: IS 15 10 Io o 05 o o-5 10 15 o O 05 10 X L L

Fig. 17. Mean increase of torque of propeller 4202.

05 10 15 05 10 IS 10 05

4

o 10L103 o

(23)

Fig. 18. Torque fluctuation of propeller 4202. 15 1O X

L

i L 100

-.-.. L 70

L

i L 50 Fn 0.145 HEAD WAVES

A

FOLLOWING WAVES

L

i L 100 I. 70

L

L 50 Fri 0170 HEAD WAVES FOLLOWING WAVES

L

L 100 . _L. L 70

L

i L 50 Fn r 0120 HEAD WAVES A FOLLOWING WAVFS 05 10 05 10 15 O O G3 5 1O-o 15 O 15,d04 û V 5 10 15 'O ° O

(24)

400 300 O w o-200 100 o X L 200 150 La O La z 100 50 o O V 20 O O o 10 O o E 3 2 o WAVE ELEVATION O 119m MAX.. 486m MAX- .478m

j

,/ L -I-

/

\

Ffl.O 120 Fn.0 145 FR03 170 FOLLOWING -WAVES

I'

I \ ¡t

4

Fn .0120 Fn .0145 Fn .0170

r

FOLLOWING WAVES / %EAD WAVES WAVE SPECTRUM

Ji

Fig. 19.

Ratio between fluctuation and mean

in-Fig. 20.

Ratio between fluctuation and mean

in-Fig. 21. Beaufort 8 wave spectrum.

crease of thrust of propeller 4202.

crease of torque of propeller 4202.

-50 o .50 TROUG L CREST 05 lo 15 05 10 (L) in rad nec1 05 10 15

(25)

w 0 40z w o o o z 14o 20 o o _o 50 lOO 150 THRUST N ONT THRUST IN TONS

Fig. 23. Thrust and torque of propeller 4202 in Beaufort 8 head waves.

200

250 40 o o o o 20 o O 40 w o o O wo 41 20 V COSkn D. 50m CALM WATER N.60.O N BEAUFORT 8 .590 V .1054V 0. 80m CALM WATER N .60.0 BEAUFORT B N 690

I

V . 1334r1 D 6.0 m CALM WATER BEAUFORT B N.726 5.820 7

H

\ +

_/

5 V D . 133k,, SOr,, CALM WATER N.725 BEAUFORT 5.820 8 -I' -n 50 100 150 200 250 TORQUE IN TONMETERS 100 150 200 250 TORQUE IN TONMETERS o 40 ft oC-) o w o w 20 50 100 150 200 250

(26)

40

Si o o o z w o

20

w o 402 w o o o o w 20o.

o 100 o o

40 u o O z wo w 20 o 100 40 o o o o 20 o o V 17.1Ro O 8.001 CALM WATER N 97O BEAUFORT n N.1030

j'

:

/ \\ V . 0 171ko 8.001 CALM WATER N97,0 BEAUFORT N1030 B

J

/' '\ V . D 132 kfl CALM WATER N.615 BEAUFORT B 11.940

/

r

', V 132ko D 75m CALM WATER BEAUFORT B N615 N.940 / -.-5° 100 150 200 250 THRUST IN TONS 50 100 150 200 TORQUE IN TONMETERS 150 200 250 300 TORQUE IN TONMETERS ISO 200 250 300 350 THRUST IN TONS

(27)

w o 20 V Il.2kn D BOW 7L

_y

THRUST N TONS

Fig. 27. Thrust and torque of propeller 4202 in Beaufort 8 following waves.

TORQUE IN TONMETERS V O . 13 4kn .8.5 81 CALM WATER N.635 BEAUFORT N.730 B I cr4 V . 134 kn D . 55m CALM WATER N.635 BEAUFORT 5.730

J

V . 11 2 kIl D. 80m CALM WATER BEAUFORT B 5.625 ! N.55 7, U 40 CALM WATER BEAUFORT 8 o N .62.5 N.65.5 L) o 50 lOO 150 THRUST IN TONS

50 lOO 150 200 250 TORQUE IN TONMETERS 50 100 150 200 50 100 150 200 250 200 2 5l 40 z o o o z o 20 o 40 w o O O o 20 o 40 o o O z w o 20 o

(28)

40 o u u O z O 20 0 100 V 14 3kT D 800 40 O O O O 20 V . 14 3 kn 0.601,1 CALM WATER N.800 BEAUFORT B NB40 I ..

1i

IT: V. lß3kn 0. 8 Orn CALM WATER N.910 ¡ BEAUFORT N.940 B

_J

V I63Rr D. BOrn I CALM WATER BEAUFORT B N.910 N.940 47/ 40 z 40 z CALM WATER BEAUFORT 8 z, u O O zw Oa N.600 N.840 u u O z w u R 20 20 50 100 50 200 250 50 100 ISO 200 THRUST IN TONS TORQUE N TONMETERS

THRUST IN TONS

TORQUE

IN TONMETERS

150 200 250 300 350 50 100 150 200

(29)

Lu u 40 bi u u 0 z u

20 o

w U 40 zbi W u O O z O bi

20 0

0 Fig. 31

Thiict and torque of propeller 4201 in Beaufort 8 following waves.

40 z w u O O w O 20 0. V 157EV O 65m CALM WATER N . 970 BEAUFORT B N=10IO V . 157kn D 75m CALM WATER Ns750 BEAUFORT8 N790 V. 157 0. 75m CALM WATER N.75.0 BEAUFORT 8 N79O

Hf

-V 157kn D 85m CALM WATER N.970 BEAUFORT 8 N1010 I

/

7L 50 100 150 THRUST IN TONS Fig. 30.

Thrust and torque of propeller 4203 in Beaufort 8 following waves.

50 100 150 200 250 TOROUE IN TONMETERS 100 50 200 250 TORQUE IN TOSMETERS 50 100 150 THRUST IN TONS 200 250 200 250 50 40 z W u u o z u O

(30)

o I 300 200 loO o 100 125 150 SPEED IN KNOTS

Fig. 32. Speed - thrust relation

in Beaufort

8 head waves for propeller 4202.

175

o loo

8 following waves for propeller 4202.

/

300 200 w z O 100 o 300 200 loo o o100 SPEED IN KNOTS

Fig. 35. Speed - torque relation

in Beaufort

8 following waves for propel 1er 4202.

FROM REGULAR WAVES

BEAUFORT 8

7,

-lf3

_w_

- --

-uuuít.uuuuí._:11--7

CALM WATLR

FROM REGULAR WAVES

BEAUFORT 8 --1/3_ _{_(} _' __ --./ --' -_____,-.__ ---CALM WATER

FROM REGULAR WAVES

BEAUFORT 8 / / r

,///

T113_ --_ av.7 7_ , oi;7 CALM WATER

FROM REGULAR WAVES

BEAUFORT B _. -___ aif3.- __--- Oaw -

--'

.4' _, ---- CALM WATER l/3 125 STESO :3 00015

Fig. 33. Speed -. torque relation

11

Bcaulbrt

8 head waves for propeller 4202.

125

15.0

lis

SPEED IN KNOTS

Fig. 34. Speed - thrust relation

in

Beaufort

125

150

(31)

PUBLICATIONS OF THE NETHERLANDS SHIP RESEARCH CENTRE TNO

PUBLISHED AFTER 1963 (LIST OF EARLIER PUBLICATIONS AVAILABLE ON REQUEST)

PRICE PER COPY DFL. lo.- (POSTAGE NOT INCLUDED)

M = engineering department S = shipbuilding department C = corrosion and antifouling department

Reports

57 M Determination of the dynamic properties and propeller excited vibrations of a special ship stern arrangement. R. Wereldsma, 1964.

58 S Numerical calculation of vertical hull vibrations of ships by

discretizing the vibration system, J. de Vries, 1964.

59 M Controllable pitch propellers, their suitability and economy for large sea-going ships propelled by conventional. directly coupled engines. C. Kapsenberg, 1964.

60 S Natural frequencies of free vertical ship vibrations. C. B.

Vreug-denhil, 1964.

61 S The distribution of the hydrodynamic forces on a heaving and

pitching shipmodel in stitl water. J. Gerritsma and W.

Beukel-man, 1964.

62 C The mode of action of anti-fouling paints: Interaction between anti-fouling paints and sea water. A. M. van Londen, 1964.

63 M Corrosion in exhaust driven turbochargers on marine diesel

engines using heavy fuels. R. W. Stuart Mitchell and V. A. Ogale, 1965.

64 C Barnacle fouling on aged anti-fouling paints ; a survey of pertinent literature and some recent observations. P. de Wolf. 1964. 65 S The lateral damping and added mass of a horizontally oscillating

shipmodel. G. van Leeuwen, 1964.

66 S Investigations into the strength of ships' derricks. Part I. F. X.

P. Soejadi, 1965.

67 S Heat-transfer in cargotanks of a 50,000 DWT tanker. D. J. van der Heeden and L. L. Mulder, 1965.

68 M Guide to the application of method for calculation of cylinder liner temperatures in diesel engines. H. W. van Tijen, 1965. 69 M Stress measurements on a propeller model for a 42,000 DWT

tanker. R. Wereldsma, 1965.

70 M Experiments on vibrating propeller models. R. Wereldsma, 1965.

71 S Research on bulbous bow ships. Part II. A. Still water

perfor-mance of a 24,000 DWT bulkcarrier with a large bulbous bow. W. P. A van Lammeren and J. J. Muntjewerf, 1965.

72 S Research on bulbous bow ships. Part II. B. Behaviour of a

24,000 DWT bulkcarrier with a large bulbous bow in a seaway. W. P. A. van Lammeren and F. V. A. Pangalila, 1965.

73 S Stress and strain distribution in a vertically corrugated bulkhead. H. E. Jaeger and P. A. van Katwijk, 1965.

74 S Research on bulbous bow ships. Part 1. A. Still water investiga-tions into bulbous bow forms for a fast cargo liner. W. P. A. van Larnmeren and R. Wahab, 1965.

75 S Hull vibrations of the cargo-passenger motor ship "Oranje

Nassau", W. van Horssen, 1965.

76 S Research on bulbous bow ships. Part I. B. The behaviour of a fast cargo liner wi,.h a conventional and with a bulbous bow in a sea-way. R. Wahab, 1965.

77 M Comparative shipboard measurements of surface temperatures

and surface corrosion in air cooled and water cooled turbine outlet casings of exhaust driven marine diesel engine

turbo-chargers. R. W. Stuart Mitchell and V. A. Ogale, 1965. 78 M Stern tube vibration measurements of a cargo ship with special

afterbody. R. Wereldsma, 1965.

79 C The pre-treatment of ship plates: A comparative investigation

on some pre-treatment methods in use in the shipbuilding

industry. A. M. van Londen, 1965.

80 C The pre-treatment of ship plates: A practical investigation into

the influence of different working procedures in over-coating

zinc rich epoxy-resin based pre-construction primers. A. M. van Londen and W. Mutder, 1965.

81 S The performance of U-tanks as a passive anti-rolling device.

C. Stigter, 1966.

82 S Low-cycle fatigue of steel structures. J. J. W. Nibbering and

J. van Lint, 1966.

83 S Roll damping by free surface tanks. J. J. van den Bosch and

J. H. Vugts, 1966.

84S Behaviour of a ship in a seaway. J. Gerritsma, 1966.

85 S Brittle fracture of full scale structures damaged by fatigue.

J. J. W. Nibbering, J. van Lint and R. T. van Leeuwen. 1966. 86 M Theoretical evaluation of heat transfer in dry cargo ship's tanks

using thermal oil as a heat transfer medium. D. J. van der Heeden, 1966.

87 S Model experiments on sound transmission from engineroom to accommodation in motorships. J. H. Janssen, 1966.

88 S Pitch and heave with fixed and controlled bow fins. J. H. Vugts,

1966.

89 S Estimation of the natural frequencies of a ship's double bottom by means of a sandwich theory. S. Hytarides, 1967.

90 S Computation of pitch and heave motions for arbitrary ship forms. W. E. Smith, 1967.

91 M Corrosion in exhaust driven turbochargers on marine diesel

engines using heavy fuels. R. W. Stuart Mitchell, A. J. M. S. van Montfoort and V. A. Ogale, 1967.

92 M Residual fuel treatment on board ship. Part II. Comparative

cylinder wear measurements on a laboratory diesel engine using filtered or centrifuged residual fuel. A. de Mooy, M. Verwoest and G. G. van der Meuten, 1967.

93 C Cost relations of the treatments of ship hulls and the fuel

con-sumption ofships. H. J. Lageveen-van Kuijk, 1967.

94 C Optimum conditions for blast cleaning of steel plate. J.

Rem-melts, 1967.

95 M Residual fuel treatment on board ship. Part I. The effect of can-trifuging, filtering and homogenizing on the unsolubles in residual fuel. M. Verwoest and F. J. Colon, 1967.

96 S Analysis of the modified strip theory for the calculation of ship

motions and wave bending moments. J. Gerritsma and W.

Beii-kelman. 1967.

97 S On the efficacy of two different roll-damping tanks. J. Bootsma and J. J. van den Bosch, 1967.

98 S Equation of motion coefficients for a pitching and heaving des-troyer model. W. E. Smith, 1967.

99 S The manoeuvrability of ships on a straight course. J. P. Hooft,

1967.

100 S Amidships forces and moments on a CB = 0.80 "Series 60"

mode] in waves from various directions. R. Wahab, 1967. 101 C Optimum conditions for blast cleaning of steel plate. Conclusion.

J. Remmelts, 1967.

102 M The axial stiffness of marine diese] engine crankshafts. Part 1. Comparison between the results of full scale measurements and

those of calculations according to published formulae. N. J.

Visser, 1967.

103 M The axial stiffness of marine diesel engine crankshafts. Part II. Theory and results of scale model measurements and comparison with published formulae. C. A. M. van der Linden, 1967.

104 M Marine diese] engine exhaust noise. Part I. A mathematical model.

J. H. Janssen, 1967.

105 M Marine diesel engine exhaust noise. Part II. Scale models of

exhaust systems. J. Buiten and J. H. Janssen, 1968.

106 M Marine diesel engine exhaust noise. Part III. Exhaust sound

criteria for bridge wings. J. H. Janssen en J. Buiten, 1967.

107 S Ship vibration analysis by finite element technique. Part 1.

General review and application to simple structures, statically loaded. S. Hylarides, 1967.

108 M Marine refrigeration engineering. Part I. Testing of a

decentraI-ised refrigerating installation. J. A. Knobbout and R. W. J.

Kouffeld, 1967.

109 S A comparative study on four different passive roll damping tanks. Part I. J. H. Vugts. 1968.

110 5 Strain, stress and flexure of two corrugated and one plane

bulk-head subjected to a latera], distributed load. H. E. Jaeger and

P. A. van Katwijk, 1968.

Ill M Experimental evaluation of heat transfer in a dry-cargo ships'

tank, using thermal oil as a heat transfer medium. D. J. van der

Heeden. 1968.

112 S The hydrodynamic coefficients for swaying, heaving and rolling cylinders in a free surface. J. H. Vugts, 1968.

113 M Marine refrigeration engineering. Part II. Some results of testing a decentralised marine refrigerating unit with R 502. J. A. Knob-bout and C. B. Colenbrander, 1968.

114 S The steering of a ship during the stopping manoeuvre. J. P.

Hooft, 1969.