The manoeuvrability of ships on a straight course

REPORT No. 99 S

August 1967

(S 2/112)

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

NETHERLANDS SHIP RESEARCH CENTRE TNO

SHIPBUILDING DEPARTMENT LEEGHWATERSTRAAT 5, DELFT

*

THE MANOEUVRABILITY OF SHIPS ON A

STRAIGHT COURSE

(DE MANOEUVREEREIGENSCHAPPEN VAN SCHEPEN BU HET VAREN

LANGS EEN RECHTE KOERS)

by

IR. J. P. HOOFT

Netherlands Ship Model Basin

Het toenemen van de grootte-van tankers brengt verschillen-de problemen met zich rneverschillen-de. Deze worverschillen-den niet alleen veroorzaakt door de beperkte waterdiepte van vele haven-toegangen in combinatie met de steeds toenemende diepgang van de schepen, maar eveneens door bet verminderen van de rrioeuvreerbaarbeid bij bet groter worden van bet schip, ook op niet beperkt water.

He dod van bet onderzoek is geweest orn de manoeuvreer-eigenschappen op een rechte koers te onderzoeken, zowel de reactie van het schip op een roeruitsiag, als de stuurvaardig-heid van de dirigerende mens in bescbouwing nemende

Het eerste aspect bestond uit het bepalen van de K- en T-waarden, als coëfficiënten van de bewegingsvergelijking voor bet sturen in bet horizontale viak, uit suurproeven met sinusoïdale roeruitslagen en uit spiraalproeven. Het tweede vraagstuk was ingewikkelder. Voor voorwerpen met een snelle stuurreactie, zoals een auto of een vliegtuig (met lage waarden voor T en hoge waarden voor K), waren de coëffi-cienten van de reactiefunctie bekend. Door extrapoleren in de richting van bogere waarden van T en lagere waarden van K, werden de coëflìciënten voor scheepsvormen gevon den. Belangrijk daarbij was, dat enkele uitkomsten van proc-ven met tankers van 50.000-100.000 ton deadweight zeer goed bleken overeen te stemmen met deze extrapolatie.

Bu het analyseren van bet sturen van bet schip kan de frequentie waarmede het schip zal worden gestuurd, bepaald worden; een bespreking voigt over de manoeuvreereigen-schappen van bet scbip op een rechte koers, waarbij de in-vloeden van bet roeropperviak, de scheepsvorm en de grootte van het schip worden bezien.

Tot slót wordt onder andere gememoreerd, dat een lagere L/B-verhouding de manoeuvreerbaarheid langs een rechte koers vermindert, speciaal voor grotere schepen en dat door het toenemen van de scheepsgrootte,, zelfs wanneer alle scheepsafmetingen naar verhoudiñg worden vergroot, de

manoeuvreereigenschappen slechter zullen worden. Zel1 is

in dit laâtste geval voor de zeer grote schepen de grootte van het roeropperviak van minder belang.

1ET NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

The increasing of the size of tankers is accompanied with a lot of problems. These are not only due to the limited depth of water of the entrances of many ports in combination with the growing draught of the vessels, but also to the decrease of manoeuvrability with the increase of the ship'i size, also in non-restricted water.

The purpose of this investigation was, to examine into the manoeuvrability on a straight course, taking into account both the- ship's response on an action of the rudder and the steering ability of the human operator.

The first aspect consisted in the determination of the K and T-values as coefficients of the equation of motion for steering in the horizontal plane from steering tests with sinusoidal rudder actions and from spiral tests. The second problem was a more complicated one. For objects with a quick response on steering as an automobile or an aircraft

(with low values of T and high values for K), the coefficients of the response function were known. By extrapolating in the direction of higher values of T and lower values of K the response coeflicients for shiplike objects were found. Impor-tant was, that some results available from tests on tankers of 50,000 up to 100,000 dwt appeared to fit very well in this extrapolation.

Analysing the ship's steering, the frequency at which the ship will be steered can be determined; a discussion follows about the ship's manoeuvrability on a straight course, taking into account the influences of rudder area, the hull form and the ship's size.

In the conclusion is mentiòned among othérs that a

decrease of the ratio of the length to the breadth decreases the manoeuvrability along a straight course especially for bigger ships and that by increasing the size of the ship, even if all the ship's dimensions are enlarged proportionally, the manoeuvrability will decrease. Even in this last mentioned case it appears that the influence of the rudder area is of minor importance for a large size of ship.

THE NET}rERLANDS.SHIP RESEARCH CENTRE TNÔ

CONTENTS

page

Summary 7

1 Introduction 7

2 Description of the model tests - 7

3 Results of the model tests 10

4 The ship's response to a rudder angle in a linear case 10

5 Approximation in the case of a non-linear response. 11

6 The steering ability of a human operator Il

7 Analysis of the ship's steering 12

8 Discussion of the ship's manoeuvrability on a straight course 13

9 Conclusions...

14

References 15

Appendix I The speed of the steered ship 17

Appendix II

Procedure for conducting overshoot tests 18

LIST OF SYMBOLS

B breadth of the ship

CB block coefficient

G response function of the rudder motion produced by a helmsman to a ship's motion

H

response function of theship's motion to a rudder motion

I

moment of inertia of the ship

K turning ability coefficient (M/N)

L length between perpendiculars

M coefficient of the móment of the rudder force

N coefficient of the nornent of the resistañce

T time constant of the ship (I/N)

T draft of the shij

TL, TN time constañts of the helmsman

a magnificatidn factór òf the helmsman

g ratio of the ämplitude of the rudder angle to the amplitude of the course angle

h ratio of the amphtude of the yawing angle to the amplitude of the rudder angle

r angular velocity of thè ship.

t time

a phase difference between ship motion and rudder rnotion

ß phase

ffeeçe betwen uddr motion and ship motion

rudder angle.

-e heading errOr

directiOn of the path that the ship has to f011ow

angle of yaw = direction of the ship to an axis of reference

THE MANOEUVRABILITY OF SHIPS ON A STRAIGHT COURSE

by

IR. J. P. HOOFT

Summary

In this investigation first K- and T-figures from the equation of motion, as. presented by NoMoTo, were determined by

means of model experiments. This was doñe for a cargoliner and a tanker respectively, for different rudder area's andspeeds.

After that the steering ability of the hüman operator was investigated as a logical consequence to the knowledge already available for fast response objects as aircrafts and automobi1es

An analysis of the ship's steering follóws, taking into accouiit both the ship's response and the response of the helmsman. At the end the manoeuvrability on a straight course of these combined responses is discussed -taking into account the influences of rudder area, hull form and ship's.size.

i

Introduction

In the past it was tried to develop a criterion -about

the manoeuvtability of ships by means of more or

less definitive manoeuvres of the ship, as defined by

KEMPF [1], GERTLER [2], NoMo'ro [3] etc. The

objection against this procedure is mainly t-bat

during these definitive manoeuvres the motion of

the rudder is rather unrealistic, being for instance

stationary or zigzag, on account of which it is.

impossible to determine the ship's response upon

the rudder motions during service conditions.

A next step to draw criteria is to look at the

behaviour of the steered ship in service conditiön.

By placing a criterion e.g. a small lane, little rudder

action, or small drop of the ship's speed etc. one

can determine an optimum adjustment of the

(automatic) pilot. Up to now there has been little

need for this in practice because ships could mostly

reach their destination whether optimum. steered

or not. Since the appearance of large tankers,

however, a very accurate steering of the ship is

needed to enable navigation iñ restricted

water-ways.

The criteria mentioned above have only been

of importance from a more or less theoretical point

of view. In practice only the opinion of the master

has been a criterion of the manoeuvrability. This

criterion mostly comes down to the principle that

a ship is said to have good steering qualities when

little action of the rudder is needed to keep her on

a straight course. Such criteria are described for

flying machines and automobiles by SEGEL [6],

who based the criterion about the manoeuvrability

of the vehicle upon the judgement of a number of

helmsmen who steered the vehicle.

In this article it will be tried to develop criteria

about the ship's manoeuvrability taking into

ac-count the ability of human beings to steer the ship.

The difficulty with this method is the large

adapt-ability of men and the large differences in taste.

Even when most of the helmsmen qualify the

ma-noeuvrability of the ship in a negative sense there

still remains the possibility that the helmsmen

change their mind when the steering of the ship

is altered by placing electronic apparatus in

be-tween the helmsman and the rudder engine

The way itt which helmsmanship is described in

this report is based on about 20 records, measured

on tankers varying in size from 50,000 dwt, to

[00,000 dwt. The results fitted so well with those

of MCRUER and KRENDEL [7] that the description

may be .used as a starting point. The results of

MCRUER were based ori tests with human beings

when steering objects with rather quick responses

such as aerOplanes.

The purpose of this investigation was to

deter-mine the ship's behaviour when steered on a

straight course by a helmsman whose- steering

abil-ity is known in a way as will be described in this

paper.

2

Description of the model tests

The tests were performed in the shallow water

laboratory of the Netherlands Ship Model Basin

at a waterclepth of 1.00 m. The width of this basin

is 15.75 m. The dimensions of the models and the

propellers are given in Tables I and II. Bodyplans

of the models (a cargo-liner and a tanker) are given

in figures 1 and 2.

During the tests, records were made of the rudder

angle, the revs./min. of the propeller, the yawing

angle, the rate of change of heading (rate of turning)

and the position. of the model. The yawing angle

and the rate of turning were measured by means of

a gyroscope. The position of the model was

8

Table I The principal dimensions of the model of a cargo. liner

Length between perpendiculars (m) - 6.6040

Breadth (m) 0.9340

Draft (m) 0.3683

Displacement (dm3) 1345.42

Wetted surface (m2) 7.7328

PropeÏler of cargo liner

Diameter (mm) 250.00

Number of blades 4

Pitch at root (mm) 220.15

Pitch at blade ip (thm) 241.63

Pitch at 0.7 R (mm) 241.50

Developed blade area ràtio 0.621

Directiòn of turning right-handed

Length between perpendiculars 6.6040 m

Breadt.h 0.9340 m

Draft 0.3683 m

curVe_of sectionaL areas

20

Fig. I Body plan of the cargo liñer model

APP FPP

Table II The principal dimensions of the model of a tanker Length between perpendiculars

Breadth Draft Displacement Wetted surface Diameter Number of blades Pitch at root Pitch at blade tip Pitch at 0.7 R

Developed blade area ratio Direction of turning (m) 7.0940 (m) 0.9420 (m) Ó.3757 (dm3) 2012.74 (m2) 10.1013 Propeller of tanker (mir) 232.73 4 (mm) 140.91 (mm) 175.46 (mm) 170.77 0.624 right-handed

Length between perpendicütars 7.0940 m

Breadth 0.9420 m

Draft 0.3757 m

curve -of sectional areas

/ / J Lb

21

3

..151O

\)/

APP FPP 20

lo

RUDDER ANGLE SINWt s.-o TIME

Fig. 3 Definition of ship's motion as a response to the rudder motion

mined by an X and Y record of a fixed point on

the model which was followed by an observer on

the carriage.

During the sinustests the rudder angle was

changed sinusoidally as a function of time.

The zigzag manoeuvres were carried out as

described in Appendix II.

3

Results of the model tests

Sinustests: The ship's response to a rudder angle is

defined by the ratio of the ship's motion to the

sinusoidal rudder motion (response function H):

course angle

7/)

sin(wt+a)

H= ...

rudder angle

(5 (5sin cot

The ship's response therefore is defined by the

amplitude ratio

/(5 and the phase difference a (see

figure 3). These items as a result of the sinustests

are plotted in diagrams i to 8 as a function of the

freqùency (see appendix III).

The ship's speed along a sinusoidal path is given

in diagrams 15 and 16 in appendix III..

Zigzag tests: The results of the zigzag tests are

given in diagrams 17 and 18. From these results

the diagrams 9 and 10 have been derived. If during

the zigzag manoeuvre the maximum rate of turning

for the given rudder angle was not reached, an

extrapolation has been carried out to determine

this maximum.

4 The ship's response to a rudder angle

in a linear case

The ship's motioñ in the horizontal plane can be

described in a simplified way by taking into account

the moment of inertia of the ship's mass, the

mo-ment of the ship's resistance against turning and

the moment of the rudder force:

d2 d

I-+ N-a- = M(5

By making use of the K and T values, a method

described by

NoMoTo

[3] this equation becomes:

Tf+r = K(5

(eq. 4-1)

yawing angle

r = d/dt = rate of change of heading

f = d2/dt2 = angular acceleration of yaw

T = time constant = inertia coefficient = I/N

K = turning ability coefficient = MIN

(5 = rudder angle

When the rudder is oscillating sinusoid ally:

(5 = (5sin cot

then the ship's response will be:

7/'=sin(wt+a)

and

r = f cos(wt+a)

with f = w.

The response of the ship to a rudder action is

defined by the response function (see figure 3):

H =

:sit+a)

= he

. . .

. (eq. 42)

(5

(5sinwt

Considering that a

from'which follows

and

7/i,

and substituting all that in equatión (4-1)

the response function becomes:

K

H=.

zw (1 + Tzw)

on account of which:

h =

K

.

(eq. 4-3)

5

When w/5 is plotted logarithmically as a func

tion of the frequency the following curve is found

corresponding to figure 4.

YAWING ANGLE () = () SIN(U)t+OE)

3

o

Log w

Log

w---Fig. 4 Rate of turning as a function of the frequency of

oscillation

For small frequencies log w/ will be equal to

log K. When the frequencies become large, then

log o/5 will be linear to log w in such a way

that:

dlogw3/5

1

d log w

The frequency wo for which the tangents a and b

cross each 'other follows from:

wo =. l/T

.

(eq. 4-4)

Since for higher frequencies the 'slope of the

loga-rithmic response factor (log w/t5 as a function

of the logarithmic frequency '(log w)

is. known,

the tangent for higher frequencies can be drawn

through the model test results 'as is done in diagrams

1 to 8 (see appendix III).

5 Approximation in the case of a non-linear

response

The above mentioned method cannot be used

with-out the following description of the non-linear

phenomena.

When the ship's response is not linear to the

rudder angle the ship will have a periodical but

not a sinusoidal motion when the rudder is

oscil-lating sinusoidally. In that case a sinus is taken of

which the differences with the actual ship's motion

over onè period are minimized. This linearisation

has been described by KOCHENBURGER [8]

(see

figure 5).

Fig. 5 Periòdic ship motion simplified by means of a

lin-earized harmonic oscillation

The amplitude of the sinus follows from:

+,z

= _fiposin

wt dwt

(eq. 5-1)

The ship's response to a sinusoidal

rudderoscilla-tion is then defined by the ratio of this average

sinus to the rudder motion.

From equation (4-3) it follows that K can be

determined when r is known as a function of the

rudder angle during a steady turning (f = 0) as

plotted in diagrams 9 and 110. K follows from a

sinusoidally oscillating rudder with an infinitely

long period (w -± 0):

b

hm 5 sin wt

w-O

The ship's rate of turning then is:

r = hm f

cos(wt+a)

w-.0

According to equation (5-l) one finds:

+:

f

i

T ..

K =- = lim

I rsinwtdwt

. .

(eq. 5-2)

O

w-O0J

The K values obtâined in this way are plotted in

diagram 11 as a function of the rudder angle.

When K is known the tangents fór low frequencies

can be drawn in the diagrams i to 8 (see Appendix

III). From the interception of the two tangents.in

these diagrams one finds the frequency wo from

which the values of T in equation (4-3) can be

determined with equation (4-4).

The steering ability of a human operator

'the behaviour of the human operator can be

analysed by measuring the rudder activity the

helmsman produces in his trials to decrease the

ship's heading error. When the heading error is

varied sinusoid ally:

e = ë sin wt

the rudder angle will change periodically and can

be approximated by:

b = sin(wt+fl)

The helmsman is de'cribed by the response

func-tion:

G b

sin(wt+ß)

- ge

e

esinwt

To detérmine G the helmsman is instructed to steer

the ship along a sinusoidal path. He will then

change the rudder ángle almost sinusoidally with

time.

12

When the direction of the path is given by:

=i= Sin oit

the rudder is set at an angle of â degrees which is

assumed to be linear to the course error ¿q and to

d

the error in the rate of turning ¿

thus:

dw

â = k2&p + k1tX

(eq. 6-1)

At the same time the helmsman will compare the

angle â at which the rudder is set with the rudder

angle â = kaçt that should be needed to steer the

ship along the given path

,

the sinusoidal varying

course,

thus: (3*_(3 =

or k3â = k3Lq7

(eq. 6-2)

The meaning of equation (6-2) is:

Needed rudder angle - actual rudder angle =

= desired change of rudder angle.

From the equations (6-l) and (6-2) it follows that

the behaviour of the helmsman can be described

by the response function:

/k2\2 k3k1

I

w2+l

/c3+ki k2

2.

-(

w2+l

=a1/l+TL20i2

_{(eq. 6-3)}

V l+TN2W2

Equations (6-l) and (6-2) can also be' explained

by a block diagram as given in figure 6.

drectior, of the ,, AP

path that the ship has to follow

d

dt

H

6 actuaL

ruOder angle

Comparison between the desired direction P and the

diriction that, according to the helmsman. Will be

attained by the actual rudder angle

Fig. 6 Block diagram of the steering action of a human

operator

Equation (6n3) has been gi'en by MCRUER and

KRENDEL [7] with the values of a, TL and TN

which they obtained from experiments during

which helmsmen were steering quickly responding

objects.

It will be clear that the action of the helmsman

depends much upon the object that he is steering.

Therefore the values of a, TL and TN given by

MCRUER and KRENDEL for the human operatór

when steering an object as is described by equation

(4-3) for low values of T and high values of K have

to be extrapolated for the steering of an object

with high values of T and low values of K

cor-responding to a large ship. In this way a, T. and

TN are found as is given in diagram 12 (appendix

III). These values are checked by some tests on

tankers of 50,000 dwt up to 100,000 dwt. The

results of these tests correspond so well with the

values of diagram 12 that these diágrams are used

for analysing the ship handling criteria in this

report.

The values in diagram 12 have to be considered

to be valuable for an average experienced

helms-man working under normal conditions. The ability

of the helmsman can be increased much if required

for certain circumstances. But then a high

per-formance of the helmsman is desired which can

never last, for a long time. The helmsman soon

becomes tired and his ability decreases quickly.

7

Analysis of the ship's steering

he way in which a ship is steered on a straight

course can in a simplified way be describçd by the

block diagram in figure 7 in which all motions of

the helmsman, the ship and the rudder are

har-monic oscillations (sinusoidally varying motions).

It then is assumed that any arbitrary motion

con-sists of an infinite number of harmonic components.

direction of the ,(Th heading error C

desired course '-" that the helmsman

wants to decrease

G: response of thehcLrnsman Huship'n response

rudder

angle5 N actual directionof the ship Lila

Fig. 7 Block diagram of the behaviour of the steered ship

In this diagram the rudder angle due to the heading

error is described as a function of the response of

the helmsman.. But in this operator response also

the transfer between the helmsman's activity and

the rudder activity is included. The distribution of

all the influences between rudder activity and

helmsman's activity lays out of the scope of this

investigation.

The actions taking place in the block diagram

can be described as follows:

The rudder action depends on the heading error:

â = G = G(-0)

(eq. 7-1)

The actual ship's heading angle depends on the

rudder angle:

From equations (7-1) and (7-2) it follows that:

t'o HG hg

1±HG

1+ge«a

.

.,.

(eq.. 7-3)

This equation can serve to derivç the condition of

course. stability of the steere4 ship on a straight

course.

When a straight course is wanted, which means

that the harmonic oscillation of the desired course

is zero (

= 0), the actual course variation (po)

also should be zero, if the factor I +HG does not

become zero

When i ±HG becomes negative or zero for the

frequency w at which a.+ß = 180° then

o will

increase even when

= O is wanted.

As is shown by CHESTNUT and MAYER {16], the

ship will be steered at a frequency for which the

sum of i and ß is. about 180° and the product of

the ship's response h and the response of the

helms-man g is equal to 1. In this case vo does not change

much even when the ship has to be kept on a

straight course. This can be made clear in the

following way. When o decreases the responses of

the ship and the helmsman will become more

in-active so that

o increases

again. When o increases

the response of the helmsman will decrease more

rapidly the heading error.o. At lastan equilibriuth

exists at which the amplitude of the ship's heading

error will be stationary. The frequency of this

sustained oscillation then also becomes stationary.

The condition of the course stability in case of a

steered ship can be reduced to the statement:

l+HG = O

The phase difference ß between the rudder

ac-tivity and the heading error as established by the

helmsman is only small and does not change much

with varying frequencies. At the frequencies at

which the ship will be steered the phase difference

a between the ship's response and the rudder angle

also does not change much with varying

frequen-cies.

Since the phase differences a and ß do nOt change

much with the frequency, the sum of a and ß will

be - 180° over a range of frequencies. In that case

the sinusoidally varying heading error of the ship

e = - o will be found for the frequency at which:

gh= i

(eq. 7-4)

as a result of which

gh eiS) = 1 and 1+HG = 0.

8 Discussion of the ship's manoeuvrability

on a straight course

From equatioñ (7-4) the frequency at which the

ship will be steered can be determined. Then also

the rudder angle amplitude, the heading error

amplitude and the amplitude of the rate of change

of heading are known.

In diagrams 13 and 14 (appendix III) the

am-plitude of the rate of change of heading =

is given as a function of the rudder angle amplitude.

In these diagrams also the amplitude of the

heading error and the frequency of the change of

heading respectively are given as a function of the

rudder angle amplitude.

In principle the heading error or the rate of

change of heading must have a minimum value

before a helmsman will respond. In general a rate

of change of heading is detected at an earlier time

than a heading error. This is very favourable

because if only a heading error should be detected

the heading error of the ship will become much

larger before a correction due to the rudder angle

will be introduced.

When the manoeuvrability of the ship is based

upon the principle that the helmsman will correct

the ship's motion when the rate of change of

heading exceeds 1/20° per sec. (this means a velocity

of about 1 m per 10 .sec. athwartships of a poin tof

thé ship at a distance of 100 rn in front of the

helmsman), the following conclusions as shown in

tables III and IV can be drawn from diagrams

13 and 1.4.

Table III The steering, of a cargo liner of about 12,000 dwt (displacement 18,599 tons) by a helmsman (see diagram 13)

From table III it follows that this ship can be kept

on a straight course with little rudder action easily.

The use of large rudders is not needed because the

ship can be handled easily from a pòint of view of

the rnanoeuvrability even with smaller rudder areas.

13

Ship speed

Rudder area

Motions of ship and rudder when the ship has to follow a straight

course amplitude of heading error amplitude of rudder angle period of oscillation 20 knots 20 knots 10 knots 10 knots 2.10% LT 2.58% LT 2.10% LT 2.58% LT 0.25° 0.30° 0.34° 0.34° 1.4° 2° 4.7° 5° 33 sec. 37 sec. 42,sec. 43.5sec.

14

Table IV The steering of different tankers by a helmsman (see diagram 14)

Hull form A corresponds to the model of which the principal dimensions are given in table II.

Hull form B has the following principal dirnnsions: Length betveen perpendiculars = 216 m

Breadth moulded

30.6 m

Draüght môulded = 10.28 m

This ship has been tested by NoMoTo.

Influence of rudder area: The 33,000 dwt tanker with

form A appears to be easy to steer on a straight

course even when the rudder area oniy amounts to

1.4% of the lateral area of the ship. At a speed

of 8 knots the ship can be kept on a straight course

without large deviations from this course with

rud-der angle amplitudes of about 13 degrees.

Influence of hull form: The 45,000 dwt tanker with

form B will be much more difficult to steer on a

straight course than the tanker of about the same

size with form A. The main difference between

both forms is a different ratio of length to breadth

of the ship:

LIB

7.50 for ship form A

LIB = 7.06 for ship form B.

Influence of s/zip size: It will hardly be possible to

steer a 300,000 dwt tanker along a straight course.

When the ratio of length and breadth .f the ship

is 7.50 rudder angles with an amplitude of about

25 degrees will be needed by the helmsman to steer

the ship along a straight course. Since 300,000 dwt

tankers are designed to have ratios of length to

breadth of 6 or less- it will become impossible to

steer these ships by means of a helmsman only. An

increase of the rudder area to improve the

ma-noeuvrability of this ship will only have a minor

effect.

9

Conclusions

A. The ship's manoeuvrability may be analysed

in the following way:

a.

determine the turning ability coefficient K

from spiraltests,

B.

determine the time constant T from sinus

tests,

determine the steering ability of the

helms-man -as a function1 of the K and T values,

determine the ships behaviour on a straight

course as a function of the ship's response

and the steering

bi1ity of the helmsman,

judge the ship's Inanoeuvrability by the

ship's behaviour on a straight course.

The steering qualities 1f a cargo liner of about

12,000 dwt, of which he model tests are

de-scribed in this report, re expected to be good.

This expectation is based upon the results given

in section 8.

The steering qualities of a tanker bf about

33,000 dwt with a ratió of length to breadth of

7.50 will be good evén, with a rather small

rudder.

When the ratio of the iength to the breadth of

the ship decreases the manoeuvrability of the

tanker along a straight course will decrease.

When the ship's size inpreases the

manoeuvra-bility of the ship will decrease, even when all

the ship's dimensions are increased

propor-tiòn4lly.

If the ship's manoeuvrabiIity should be analysed

as stated in conclusion A, i

will be appropriate to

make a more extefisive stuthr about the Influences of

the ship's form upon the maoeuvrabi1ity. Asa start

the influence of the parameters LIB, B/ T and CB

upon the ship's manoeuvrbility should be

inves-tigated more in detail.

Also the influence of

xternal forces on the

behaviour of the ship steerd on a straight course

bas to be analysed.

Displacement in tons - - -Hull form Speed in knots Rudder area

- Motions of ship and ruddér when the

ship has to follow a straight course amplitude of

heading error

amplitude of

rudder angle oscillationperiod of

41,859 -41,859 41,859 41,859 368,835 56,500 - A A A A A B 16 16 8 8 11.5 17.6 1.44% LT 1.77% LT 1.44% LT 1.77% LT 1.77% LT 1.40% LT 0.35° 0.35° 0.43° 0.42° 0.50° 0.90° 4° 3:7° 13° 12° 24° 4.5° 45 sec. 41 sec. 54f sec. 55 sec. 66 sec. 105 sec.

'5

Rférences

9. DIEUDONNÉ,J.: Note sur la stabilité du régime de route

des navires. Association Technique Maritime et

1. Karsp, G.: Systematische Aùswertung technischer Er- Aéronautique, 1949.

fahrungen in der See- und Binnenschiffahrt. Werft,

Reederei uñd Hafen, 1935. 10. Nossoio, K.: Directional_{steered ships with particular reference to their bad}stability of automatically

2. GERTLER, M. and S. C. GOVER; Handling quality cri-teria for surface ships. Report 1461 of the David

performnce in rough sea. Report 1461 of the David Taylor Model Basin.

Taylor Model Basin. _{11. EDA, H. and C. L. CIt&HE: Steering characteristics of}

3. Norioio, K. c.s.: On the steering qualities of ships. ships in calm water and waves. Transactions of the

4.

International Shipbuilding Progress, 1957.

DAvmsor, K. S. M. and L. SCHIFF:

Turning and

Society of Naval Architects and Marine Engineers,

1965.

5.

course-keeping qualitiès. Transactions of the Sò-ciety Of Naval Architects and Marine Engineers,

1957.

NORRBIN, N. H.: A study of course keeping and

ma-12. BitARD, R.: Manoeuvring of ships in deep water, in

shallów water and in canals. Transactions of the Society of Naval Architects and Marine Engineers,

1951.

noeuvring performance. Publ. of the Swedish State

Shipbuildipg Experimental Tank, 1960. 13. SHIBA, H: Model expriments about the manoeuvra-_{bility and turning of ships. Report 1461 of the David}

6 SEGEL L Ship manoeuvrablllty as influenced by the

transient response to the helm. Report 1461 of the _14.

Taylor Model Basin.

Wu, T. YAO,ASU: SwimmÌng of a waving plate. Journal

David Taylor Model Basin.. _{ofFluid Mechanics 10 (1961).}

7. MCRUER, D. T. and E. S. KRENDEL: The human

oper-ator as a servo system element Journal of the

Franklin Institute, Vol. 267.

l5 ABBOTT,J. H. añd A. E. VON DOENHOFF: Theory Of

wing sections. Dover publications, New York. 8. KOCHENBURGER, R. J.: Frequency response method of

analysing and synthesizing contac'tor servomechan-isms. American Institute of Electrical Engineers,

1950.

16. CHESTNUT, H. and R. W. MAYER: Servomec.nisms

and regulating system design. Vol. II, Chapter 8. John Wiley & SOns Inc., New York; Chapman & Hall Ltd., London 1955.

.16

The speed of the steered ship

When the rudder angle changes continuously, the

direction of the ship's speed relative to the ion-.

gitudinal axis of the ship also changes continuously

The drift angle

causes an increase of the ship's

resistance This increase as a function of the drift

angle e is measured for instance by BRARD [12].

The resistance of the ship will also he increased by

the rudder. The resistance of the rudder as a

func-tion of thé angle of attack of the waterfiow can be

deduced from ABBOTT and VON DÔENHOFF [15].

When the rudder is set at a fixed angle the drift

angle will also become constant. The loss in ship

speed due to the total increase of the ship's

resis-tance has been measured by SHIBA [13] for the

case of a constant rudder angle. He also measured

the change in the drift angle as a fúnction of time

when the rudder angle was suddenly changed

If the rudder angle is not constant, it might be

possible that the oscillations of the rudder and the

ship take part in the propulsion of the ship. Ac

cording to WU [14] the. following formula for the

thrust of a waving plate with â linearly varying

amplitude can be used:

P = eU2hc{bo2 T1(ft) +b12 T2(Q,k) ± bob1 T3(,,)}

In which b0 and bi are factors which define the

motion of the plate:

y(x,t) = (/2cbo+bix)sin wt

APPENDIX I

The other' symbols are defined by:

P

thrust delivered by the waving plate,

U = velocity of the plate,

a = wc/2U,

c = span of the plate,

Ii = height of the plate,

w = frequency of oscillation,

k = O for a fiat plate,

y

athward motion of the plate,

x = distance from the centre of the plate.

T1, T2 and T3 are given by Wu in diagrams The

thrust delivered by the oscillating rudder in a

potentional flow then becomes:

Pr =

U2ch52T2 (Ti nd T3 can be neglected)

in which T2 remains negative for a < 1.8. This

means that the resistance f the oscillating rudder

is larger than the resistancç of rudder set at a fixed

the thrust delivered by the oscillating ship in

a

potential flow will become:'

=

U2chë2(1/4Ti±D2±i/2Ts)

The change of the velocity due to the sum of the

resistances of the oscillatixg ship and the rudder

añd the values of Pr and P8 are calculated for two

cases ân

are plotted in digram 19. The rsu1t of

this calculation is used on1ly as an explanation of

the results of the hiodel tegts as given in diagrams

15 and 16.

Procedüre for conducting overshoot tests

The propeller speed. is adjusted to a number of

revolutions required to give the ship model a

predetermined speed..

Before starting the manoeuvre the model is

brought to a straight course at a speed

men-tionedunder item 1.

After steady . conditiòns on a straight course

have been established, the rudder is put to a

degrees port. As soon as the model has reached

a predetermined heading angle of ß degrees,

the rudder is automatically put over to a

I-o o.. &LIW _j _l . L

ZZ

.4 o

00

40

a

TIME INITIAL COURSE HEADING ANGLE RUDDER ANGLE OVERSHOOT ANGLE

Fig. 8 Presentation of a zigzag manoeuvre

APPENDIX II

degrees starboard; when the model has reached

a heading angle of j degrees to starboard, the

rudder is put over to a degrees port and so on.

During this manoeuvre the following items are

recorded:

rudder angle;

heading angle with respect to the initial

course;

rate of change of heading (angular turning

velocity of the model).

The overshoot manoeuvre is shown

diagram-matically in figure 8.

PERIOD

OVtRS4OOT TIME

(D z z D U. o w I- 4 Il. o w o D

I----J

Q. X 4

_g0o _-loop

0.3

oPHASE DIFFERENCE BETWEEN MAXIMUM RUDDER ANGLE AND MA X I MUM COURSE ANOL E

o2O°

CALCULATED

-

So

UUUUumu

iuuuaun

-.ui-..i-....-..u--Diagram i

Resûlts of sinus tests

K15 j; :i 1(5 10 RUDDER AÑGL AMPLITUDE +

MODEL OF A CARGO LINER RUDDER AREA 2:10 LT MODEL SPEED 2l0m/sec

-200 o 15° + 100 50 I.e. io 3 0.2 (D z z D I- Ii. o 'w U- o Ui Q D -J Q. X 4 t Ui o D I- -i Q. X 4 -q 0.3 0.1 (D z 4 W o Q D 0.05 rio 2O1

MODEL OF A CARGO LINER RUDDER. AREA

2.10% LT MODEL SPEED 1.05 rn/sec. RUDDER ANGLE AMPLITUDE 20° o o 15 o + 10° Q 50 o i 05 FREQUENCY W RAISEC.) Diagram 2

Results of sinus tests

ui s... sn

= PHASE ANGLE DIFFERENCE AND MAXIMUM BEtWEEN COURSE MAXIMUM ANGLE RUDDER

Pl5I

..._....__...

ssl

....__

CALCULATED:

i__

-2O° 15

l°

-

-- ._.1I

800 01 05

10

2.0 01 05 10 20 FREQUENCY W

(RAD/SEC)-t

0.2 I3 IO o 0.5 1.0 20 10 2.0 w 0 0.1 D Q- X 4 w -J ID z 4 0.05 w Q Q D

180°

03 0.2

.3

z z

0.1

DD I.- u_ - o ui< 4-. 4 1L 04

W 05

oui DO I-D z 4

U PHASE DIFFERENCE BETWEEN MAXIMUM RUDDER ANGLE

AND MAXIMUM COURSE

NG E

- 10°

CALCULATED 25

_,.

--...--....-...-....--

--..I-.u-...-....--W o D I- Q. z 4 ¶ 80° 03 0.2 I J40 ₃ (Q Z ZW. o,

D D I-,-. u - 0 _ui< I-<W u-Z

04

005

o O D

01

-....--...-....-....--oPHASE DIFFEREN E BETWEEN MAXIMUM RUDDER ANGLE AND MAX I MU M COURS E AN G L E

.l_...._...__

100 CA CULA ED

uuiau.a

A

uIbSUU

I-MODEL OF A CARGO LINER RUDDER AREA 2.58% LT MODEL SPEED 1.05 rn/s.c.

§°RUDDER ANGLE AMPITUDE:

A20° o 15° + 100 I I

i

45e A 5 MODEL RUDDER OF AREA A CARGO 2.58% LINER 15

RUj:iT:

-: ¿50, al 0.5 15 2.0 0.1 Q5 . 10 2.0 FREQUENCY W (RAD/SEC)-FREQUENCY W (RAD/SEC) Diagram 3

Results of sinus tests

Diagram 4

Results. of sinus tests

_900

go.

01 05 15 2.0 0.1 05 10 2.0

i.& Ito 3 i 0.2 z D D

I

u_ û o, E w' < i- 4 w 0.1 LS IL Z

04

w o D I- 1 o- E 4 w o o D 0.05 a3 Diagram 5

Results of sinus tests

t, z z D u. o w 4 U- o w o D, Q.' z 4 o D -J a- X 4 -90 -18 3 0.2 UI 0.1 t, z 4 w o o D 0.05 i-Kt5

- i.

§ :RJD ANGLE AMPLITUDE: A _o e 17.5 150 a 12.5 01 05 FREQUENCY W (RAD/SEC.) Diagram 6

Results of sinus tests

_...._ ..._.._...Bi__

PHASE ANGLE AND

DIFFERENCE MAXIMUM BETWEEN COURSE MAXIMUM RUDDER ANGLE L

U

17.5

- i2S0

CALCULATED

1° -.

L

iii

IO . =PHASE ANGLE AND DIFFERENCE MAXIMUM BETWEEN COURSE MAXIMUM ANGLE RUDDER o20°

d

-100

uuriu .o CALCULATED

-

-180

up

.

UURIM' U

...

_{__. _U.._...._ ...__}

K10 ,. MODEL RUDDER OF A AREA SPEED MODEL 1 1 TANKER ¿%LT 57 mf sec K'

.\20

RUDDER ANGIE AMPLITUDE

20°

015°,

f

*0

01 0.5 10 20 0.3

MODEL OF A TANKER RUDDER AREA 1LL% MODEL SPEED 0.7,85 rn/sec

LT 0.1 0.5 10 20 1.0 2.0 0.1 0.5 FREQUENCY W (RAD/SEC.) 1.0 20

3 0.2 (0 Ui,

z0

I-

'-:

U-a- o w '-w

4-j

(0 z 0W

-0

0.05

_

a

PHASE D FFERENCE BETWEEN

ANGLE AND MAXIMUM

COURSAAN RUDDE R 6 = 200 WO CALC A ED UL T

.uu...a...uu.

2 K15 1<10

MODEL 0F A TANKER RUDDER AREA

1.77'/ LT

MODEL SPEED

1.57m/sec

61RUDDER ANGLE AMPLITUDE

A20° O 5° .1_ 10 (D z Z0ßS -J U-0. oZ 4 w -W 4J a:" U-z o Z 4

aP ASE DIFFERENCE BETWEEN MAXI UM RUDDER ANGLE

AND MAXIMUM COURSE

.i..0

20 CA C .A ED

uuusiuuuu

Kic s-K20 A

MODEL OF A TANKER RUDDER AREA 1.77 0/o LT

±

o

15°

+ 100

Diagram 8

Results of sinus tests

01 FREQUENCY W(RAQ/SEc.) 0.5 10 20 Diagram 7

Resûlts of sinus tests

0.1 05 10 2.0 02 01 0.5 10 2.0 FREQUENCY W (RAD/SEC) t 0.1 le- KO a ¶ 0.3 al 05 10 2.0 5 rn/Se AM 01.ITUD MDDrL PE1D r7 5=RUDDER ANFL A 200 00 _1800 L _1800

04 02 0' _{02 Oh 08}

20°

MODEL OF O MODEL

MODEL

A CARGO' _{SPEED SPEED}

LINER 210 rn/sec. 1O5m/sec. -RUDDER AREA 210°/oLI RUDDER' AREA 2.58 °/.tT

z

STARBOARD' MODEL OMODEL °MODEL OF A SPEED SPEED TANKER 1.57 0.785

rn/sec

rn/sec

o z

z

HRUDDERAREÄ'1.44'°/.LT

I

RUDDER AREA 1.77 0/0 L o O -'D'

z

--STARBOARD----PORt

O. O 0. _0.4 0.6 0.6 Oh 0.2 o 0.2 0.6 100 20° 150 100 5° 0° 5° RUDDER ANGLE Diagram 9

'Rate ofturningas a functionof therudder angle

100 15° 200 200 15° 100 50 0° 50 RUDDER ANGLE

_. 0.6

z

w. u w

o

u

0.7 0. 0.1 O 00 50 15

RUOOÊR ANGLE AMPLITUDE

(5)-Diagram 11 Turning ability as a function of the rudder angle

MODEL OF A CARGO LINER

MO DEL SPEED 210 m/ RUDDER

l238!iLT

2.10°!. ÁREA 1.1 SPEED 105m ________ MODEL

i-_-_...---_--

-

2.!.

10° LT 258°I.LT1-_______________ MÖDEL DF -A TANKER

L

MODEL SPEED 1.57 RUDDER AREA 1-77_!.LT

I-MODEL SPEED O.l8smIsec.

1.4 hiT 1.L.1. LT 0.9 0.8

z

iL' U. U.J LI. w

o

L) 0.2 i-m .4: 0.1

z

o

150 _.10& 501

0

0.001

\

RESPONSE OF THE HELMSMAN TO A COURSE ERROR:

1iì2

c

V1.TN2w2

0.01 K 01 20 10 TL.TN

RESPONSE 0F THE HELMSMAN TO A COLASE

ERROR_a\ /14.TIw2

Vi.w2

T

/

10

- T

100 Diagram 12

10 KNOTS

0.2

+ POINTS AT WHICH

(I)1°

SPEED OF SHIP 20 KNO1S

1.0

SPEED OF SHIP 10 KNOTS

-0.1 's SPE SPEE D OF D OF SHIP 20 KM OTS SHIP 10 KNOT S Diagram 13

Cargo liner steered on a straight course by a helmsman

Amplitudeofheading error and frequency ofchangc of heading as

Amplitude of rate of change of heading as a function of the rudder

a function of the rudder angle amplitude

angle amplitude 0. 0.02 o 3

f

3 O POINTS AT WHICH W 0.0 5°/sec. 10° 5 20° 10° S 20° RUDDER AREA RUDDER AREA

- 2.10/.LT

210'/.LT 2.58 Y. LT 2.59/. LT

DISPLACEMENT OF SHIP 18599 TONS

DISPLACEMENT OF SHIP 19599 TONS

SPEED OF SHIP

0.2

Diagram 14

Tanker steered on a straight course by a helmsman

Amplitude of heading error and frequency of change of heading as

Amplitude of rate of change of heading as a function of the rudder

a function of the rudder angle amplitude

angle amplitude 0.015 001D 000 o 5

+

POINTS AT WHICH HULL SPEED DISPLACEMENT FORM OF "A SHIP .15 41859 KNOTS TONS -HULL £18 59 'HULL .368935

FORM _{8 KNOTS} TONS FORM"A"

115 KNOTS TONS

-.

_.__-.-HULL. 17.5 FORM"B" KNOTS H 56500-TONS

-

HULL 41859

FORM"' _1SKNOTS TONS

--H

---.--.-__

HULL 368835 HULL . 418 FORM"ß _{B KNOTS} 9 TONS 8KNOTS FORM'' TONS POITS-AT WHICH WI1)o005°/jec. ÑULL FROM K' ULL FROM"8"AcCORDING ACCORDING TO THE MODEL _TO A SHIP TESTED BY N TESTED BY NOMOTO S;M:B

.j

H'

HULL

iÍ

iiiI"iÌii

41859 HULL FORM. TONS ! _{HULL FORM} TONS A

--11

368835 RUDDER AREA RUDDER AREA 1.40 LT 140/.LT

- - - 144%

LT 1.44/. LT 1.77'/. LT 1.7 7/. LT 100 200 100 20° 0.2 0.1

RUDDER AREA LID 'Io LT

OES

10

FREQUENCY w IN

RAD./SEC.-MODEL OFA CARGO LINER

2.0 1.0

u

u,

RUDDER AREA 2.580/oLI

05

10

--FREQUENCY W IN RAD./SEC.

Diagram 15

Modelispeed asa function of thefrequency of the rudder oscillation at a constant number of rçvs/min of the propeller

2.0 w u,,. 15

z

1.0 E

WrH

SPEED'OF COURSE

THE MODEL ONA

THE RUDD

SRAIGHT

R AMIOSHIP

- .

RUDDER ANGLE AMPLITUDE

o 150

+10o

fl

5'

X25°

-A

2'.

+

SPED

COJRS

ÓF ÏE

WITft THE

MÓDE RLDDER ON o STRÄIGÑT _AMJDSHIP

Di

-c O A

RUDDER ANGLE AMPLITUDE

ot5

+10

OS

o

l

a -. 2G

-RUDDER AREA 1.44 f/.LT

RUDDER AREA 177/.LT

2.0 05 lOE FREQUENCY W IN RADJEC MODEL OF A TANKER

as

to

FREQUENCY W IN RAD/SEC. Diagram 16

Model speed as a function of the frequency of the rudder oscillation at a constänt number of revs-mm

of the propeller 2.0 _1.5 1.0 0s 'oF COURSE Will

- SPEED

thE

MooE[

THE RUDDER ON A STRAIGHT AMIDSHP

+

+

+

100

RUDDER ANGLE AMPLITUDE

z0p A

o15!

17.50 ø

+100

o 12.5

H

17.5° o

__._L SPEED

OJR5

'oF THE WITH

MODEL ON A STRÄIT

THE RUDDER AMIOSHIP

-4flO U

°

.:

20°

-RUDDER ANGLE AMPLITUDE

20°

15°

+10.0

--o -200

11E

0.5

300

u

w U)

z

2OO

o

w a- I 100 1.0 w 005

J

CD

z

4

o

T

u, w

>

o

o MOOEL OF A TANKER

HEADING ANGLE AT WHICH THE RUDDER IS PUT OVER:

30 1001

ii).

in,

z

X, _{IO X} (n,

wO

o

SO DiagEam 17 Results f Overshoot tests

SPEED OF SHIP 16 KNOTS

ANG TIME LE OVERSHOOT 200 O

u

w U)

z

100

o

U) w w w

0.

z

0.5 CD

z

I

o o

T

u, w

o

SPEED OF SHIP 8 KNOTS

OVERSAOOT TIME

'0

OVERSHOOT

--ANGLE

/

-'

20 10 RUDDER ANGLE O 20 10 RUDDER ANGLE

t50

25 o OVERSHOOT. TIME -z OVERSHOOT ANGLE o lo

RUDDER ANGLE

MODEL OF A CARGO LINER

HEADING ANGLE

t WHICH THE

RUDDER IS PUT OVER.3°

SPEED OF SHIP lo KNOTS

20 ?00 1200 loo 100

o

w Q. o :io 10 05 O O Diagram 18

Results of overshoot tests

RUDDER. ANGLE.

50

SPEED OF SHIP 2OIKN OIS

RTUDDER AREA

i

!PERIOD

uhupÍÌiÌ'

uuuìuuu

OVERSHOOT TIME

,uI .11:

OVERSHOOT ANGLE

O 10 20

u

w

z

25

w

X

I- s.-

o o

z

In w

125

¡

loo 75: 50 o

MODEL OF A TANKER MODEL SPEED 1.57m/sec;

20°

0.5

FREQUENCY W (RAD/SEC.)

Diagram 19 Calculated speed V1 of the model with a

sinus-oidally oscillating rudder, as a function of the speed V of the model restráined from sideway motions and with rudder in zero positiôn

PUBLICATIONS OF THE NETHERLANDS SHIP RESEARCH CENTRE TNO

(FORMERLY THE NETHERLANDS RESEARCH CENTRE TNO FOR SHIPBUILDING AND NAVIGATION)

M = engineering department S = shipbuilding department

C = corrosion and antifouling department

PRICE PER COPY DFL.

IO.-Reports

i S The determination of the natural frequencies of ship vibra-tions (Dutch). H. E. Jaeger, 1950.

3 S Practical possibilities of constructional applications of alu-minium alloys to ship construction. H. E Jaeger, i 951. 4 S Corrugation of bottom shell plating in ships with al1we1ded

or partially welded bottoms (Dutch) . H. E. Jaeger and H. A. Verbeek, 1951.

5 S Standard-recommendations for measured mile and endur-ance trials of sea-going ships (Dutch) . J. W. Bonebakker, w. j. Muller and E. J. DieM, 1952.

6 S Some tests on stayed and unstayed masts and a comparison of expeHmental resuits and calculated stresses (Dutch) . A. Verduin and B. Burghgraef, I 952f

7 M Cylinder wear in marine diesel engines (Dutch). H. Visser,

1952.

8 M Analysis and testing of lubricating oils (Dutch). R. N. M. A.

Malotaux and J. G. Smit, 1953.

9 S Stability experiments on models of Dutch and French stan-dardized lifeboats. H. E. Jaeger, J. W. Bonebakker and J. Pereboom, in collaboration with A. Audigé, I 952.

I O S On collecting ship service performance data and their analysis. J. W. Bonebakker, 1953.

i 1 M The use ofthree-phase current for auxiliáry purposes (Dutch). J. C. G. van Wijk, 1953.

12 M Noise and noise abatement in marine engine rooms (Dutch). Technisch-Physische Dienst TNO-TH, 1953.

1 3 M Investigation of cylinder wear in diesel engines by means of laboratory machines (Dutch) . H. Visser, I 954.

14 M The purification of heavy fuel oil for diesel engines (Dutch). A. Bremer, 1953.

15 S Investigations of the stress distribution in corrugated bulk-heads with vertical troughs. H. E. Jaeger, B. Burghgraef and I. van der Ham, 1954.

16 MAnalysis and testing of lubricating oils II (Dutch). R. N. M. AMâJotaux and J. B. Zabel, 1956. -17 M The application of new physical methods in the examination

of lubricating oils. R. N. M. A. Malotaux and

F. van

Zeggeren, 1957.

18 M Considerations on the application of three phase current on board ships for auxiliary purposes especially with regard to fault protection, with a survey of winch drives recently ap-plied on board of these ships and their influence on the gene-rating capacity (Dutch). J. C. G. van Wijk, 1957.

19 M Crankcase explosions (Dutch). J. H. Minkhorst, 1957. 20 S An analysis of the application of aluminium alloys in ships'

structures Suggestions about the riveting between steel and aluminium alloy ships' structures. H. E. Jaeger, 1955. 21 S On stress calculations in heliocoidal shells and propeller

blades. J. W. Cohen, 1955.

22 S Some notes on the calculation of pitching and heaving in longitudinal waves. J. Gerritsma, 1955.

23 S Second series of stability experiments on models of lifeboats. B. Burghgraef, 1956.

24 M Outside corrosion of and slagformation on tubes in oil-fired boilers (Dutch). W. J. Taat, 1957.

25 S Experimental determination of damping, added mass and added mass moment of inertia of a shipmodel. J. Gerritsma,

1957.

26 M Noise measurements and noise reduction in ships. G. J. van Os and B. van Steenbrugge, 1957.

27 S Initial metacentric height of small seagoing ships and the inaccuracy and unreliability of calculated curves of righting levers. J. W. Bonebakker, 1957.

28 M Influence of piston temperature on piston fouling and piston-ring wear in diesel engines using residual fùels. H. Visser,

1959..

29 M The influeñce of hysteresis on the value of the modulus of rigidity of steel. A. Hoppe and A. M. Hens, 1959.

30 S Ari experimental analysis of shipmotions in longitudinal re-gular waves. J. Gerritsma, 1958.

31 M Model tests concerning damping coefficient and the increase in the moment of inertia due to entrained water of ship's propellers. N. J. Visser, 1960.

32 S The effect of a keel on the rolling characteristics of a ship. J. Gerritsma, 1959.

33 M The application of new physical methods in the examination of lubricating oils (Contin. of report 17 M). R. N. M. A.

Malotaux and F. van Zeggeren, 1960.

34 S Acoustical principles in ship design. J. H. Janssen, 1959. 35 S Shipmotions in longitudinal waves. J. Gerritsma, 1960. 36 S Experimental determination of bending moments for three

rnQdelS of different fullness in regular waves. J. Ch. de Does,

1960.

-37 M Propeller excited vibratory forces in the shaft of a single screw tanker. J. D. van Manen and R. Wereldsma, 1960. 38 S Beamknees and other bracketed connections. H. E. Jaeger

andJ.J. W. Nibbering, 1961.

39 M Crankshaft coupled free torsional-axial vibrations of a ship's propulsion system. D. van Dort and N. J. Visser, 1963. 40 S On the longitudinal reduction factor for the added mass of

vibrating ships with rectangular cross-section. W. P. A. Joosen andJ. A. Sparenberg, I 961.

41 S Stresses in flat propeller blade models determined by the moiré-method F. K. Ligtenberg, 1962.

42 S Application of modern digital computers in naval-architec-' tare., H. J. Zunderdorp, 1962.

43 C Raft trials and ships' trials with some underwater paint. systems. P. de Wolfand A. M. van Londen, 1962.

44 S Some acoustical properties of ships with respect to noise control. Part I. J. H. Janssen, 1962.

45 S Some acoustical properties of ships with respect to noise control. Part II. J. H. Janssen, 1962.

46 C An investigation into the influence of the method of applica-i tion on the behaviour of anti-corrosive paint systems in sea-' water. A. M. van Londen, 1962.

47 C Results of an inquiry into thè condition of ships' hulls in relation to fouling and corrosion. H. C. Ekama, A. M. van Londen and P. de Wolf, 1962.

48 C Investigations into the use of the wheel-abrator for removing rust and millscale from shipbuilding steel (Dutch). Interim report. J. Remmelts and L. D. B. van den Burg, 1962. 49 5 Distribution of damping and added mass along the length of

a shipmodel. J. Gerritsma and W. Beukelman, 1963. 50 S The influence of a bulbous bow on the motions and the

pro-pulsion in longitudinal waves. J. Gerritsma and W. Beukel-man, 1963.

5 1 M Stress measurements on a propeller blade of a 42,000 ton tanker on full scale. R. Wereldsma, 1964.

52 C Comparative investigations on the surface preparation of shipbuilding steel by using wheel-abrators and the application of shop-coats. H. C. Ekarna, A. M. van Londeri and J. Rem-melts, 1963.

53 S The braking of large vessels. H. E. Jaeger, 1963.

54 C A study of ship bottom paints in particular pertaining to the behaviour and action of anti-fouling paints. A. M. van Lon-den, 1963.

55 S Fatigue of ship structures. J. J. W. Nibbering, 1963. 56 C The possibilities of exposure of anti-fouling paints in Curaçao,

Dutch Lesser Antilles. P. de Wolf and M. Meuter-Schriel,

1963.

57 M Determination of the dynamic properties and propeller ex-cited vibrations of a special ship stern arrangement. R. We-reldsma, 1964.

58 S Numerical calëulation 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. Vreugdenhil, 1964.

61 S The distribution of the hydrodynamic forces on a heaving and and pitching shipmodel in still water. J. Gerritsma and W.

Beukelman, 1964.

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

1964.

63 M Corrosión 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 sorne recent observations. P. de Wolf,

1964.

65 S The lateral damping and added mass of a horizontally oscil-lating shipmodel. G. van Leeuwen, 1964.

66 5 Investigations into the strength of ships' derricks. Part I. F. X. P. Soejadi, 1965.