Metacentric height and rolling period. A study on the rolling motions of a fishing vessel under different conditions

Benam ng

Proj. 8: The Stability of Fishing Vessels Fisheries Directorate

Technical Research Dept.

Auteursrccht voorbchouden vogcns de wet

Formaat

A4

Rangschikmerk

study the roll in,c moti on:

of shin,z ves1

under-diffey-ent c:ondj t ions

b y

i'.

de i-eeÌ

Schaa Gecontroeerd Getekend Gezien

Schau Auteursreeht voorbehouden volgenu e wet Getekend

BOLS ed amidships lent coefficient ficient amidships

ected for free iurfaces

ertia of a free surface ships on the line of ide of the shell

K (baseline)

ne

of gyration of the vessel he hydrodynamic mass

he vessel including the

he vessel near the quay

culars to crest Gecontroleerd Gezien Forcnaat

A4

Rangchikmerk B CB CM C r CU Benaming AE (FA) A0 (F) Cw D GM GM C LIST OF S

expanded blade area disc area

breadth moulded, measur block coefficient

midship section coeffic longitudinal prismatic rolling coefficient the upperdeck area coef waterline coefficient depth moulded, measured diameter of propeller metacentric height

inetacentric height corr

effective depth (Kato) transverse moment of in

K keelpoint measured amid

intersection of the ins

KG centre of gravity above

KM metacentre above baseli

K real transverse radius

xx K' radius of gyration of t K radius of gyration of t xxJ-hydrodynamic mass K radius of gyration of t q

LOA length overall

length between perpendi

Benaming length of waterline 1 centre of buoyancy oserv-ations itch ncounter ling period

jod (over and back) jod measured at sea

of rolling period at sea, calculated N observations

e vessel

ades of' propeller

readth y ard r ships ctor (Kato) due to gravity water rance, half

istance between two points

ights iation mean value Formaat

A4

Rangschikmerk L LCB N P TE T T0. "2 2sea T,1 "2 N V z b C d d a d ai

d.

mid dw f g h 'E i p s X longitudina number of' b propeller p period of e wave period natural rol rolling per

rol1ng per

mean value by means of speed of th number of b classified wave veloci draught for draught aft mean draugh draught ami deadweight freeboard/fa acceleration depth of the angle of ent horizontal d inclining we standard dey ari t haie tic al

Auteursrecht voorbchouden volgens de wet Getekend Gezien Schaal Gecontroleerd

I

/4

7V max III specific gravity displacement (weight) wave direction angle

3,14....

algebraic som

angle of roll, heel or list mean roll angle

mean roll angle calculated by means of N observations maximum roll angle

angle

< 4°

The I.T.T.C. (International Towing Tank Conference) standard symbols have been used as far as it was practical and possible.

Benaming

Formaat

A4

Rangachik me rk Auteursrecht voor6chouden volgens 4e wet Getekend Gezien

page

I INTRODUCTION i

II RESEARCH

General

Rolling period and initial aetacentric height Description of the vessel

Recording of' rolling periods

III HEELING TEST

IV ROLLING TESTS IN HARBOUR ₈

Loading conditions

Comparison of measurements with roll recorder and stopwatch

Free and forced rolling motions

Influence of' bilge keels

The influence of the waterdepth and the vicinity of a quay or shore on the rolling period

6, Final results (teste in harbour)

V THE INFLUENCE OF THE POSITION OF THE BOOMS OF A BEAN

TRAWLER ON THE RADIUS OF GYRATION ₁₇

Benaming

Scheal Auteursr.cht voorbshouden volgens de wet Geteoend

Gecontroleerd Gezien

Forfnaat

A4

Rangchikmerk

VI ROLLING TESTS AT SEA 19

Loading conditions

Measurement of rolling periods at sea

Statistical analysis of the rolling motion Number of observations

The influence of the wave direction with respect to the vessel

Fishing

The influence of the speed of the vessel on the rolling motions

Final results (tests at sea)

VII THE CORRELATION BETWEEN THE ANGLE OF ROLL AND ROLLING

VIII CONCLUSION 1, General

Degree of accuracy

Metacentric height and rolling period

IX REFERENCES 33 I Benaming Gecontroleerd Gezien Foroiaat

A4

Rangschikmerk 30 Schaal Aut.ursrecht voorbehouden volgens de w.t Getekend

The purpose of this study was to investigate whether it is possible to determine the metacentric height "î" within reason-able limits of accuracy by measuring rolling periods under

different working-, loading- and weatherconditiona.

To find a satisfactory stability for fishing vessels is of most importance. There is a need to find a simple method to

determine and/or to check the initial metacentric height of a vessel. The required and executed stability calculations only give information about a small number of predicted

loadingcon-ditions.

A fishing vessel with "reasonable stability" can b. very quickly transformed into a vessel with "insufficient stability" by incorrect loading and/or wrong use of fuel and watertanks, and the fact that the centre of gravity above the baseline has the tendency to rise during the first year (extra fishing gear, spare parts, etc.).

Only when stability criteria can be found which take into account the local conditions, as type and class of vessel, specific fishing methods and weather- and sea conditions, it will be possible to execute stability calculations for fishing vessels which approximate the real circumstances.

II RESEARCH 1. General

The first series of tests with a Dutch sidetrawler took

place from 8 up to 16 July,

1968.

The research was divided in two main groups, viz.: The tests to be executed in the harbour of IJmuiden

(Netherlands); and

The tests to be executed on the North Sea between

IJnnziden and Den Heider about 8 miles offshore.

The above mentioned division created the possibility to compare the results obtained in harbour (smooth water) and at

sea.

Benaming

Forrnaat

A4

Rangschikmerk

Auteursrecht voorbehouden volgens de wet Getekend Gezien Schau Gecontroleerd

-2-REC.PAPER

ROLL RECORDER

H

i

i

¡ A1Ii

I'

AIU!

__.___._

.i

-.

a.v.

_a.sva.0

r-u,

-

_{_.._I_________,__I__v__}

______

Z:=:-:w=u--'--

---_.._._w_____

.-u

V---

-.---

a

..

-f

_.

- .-2.

scale

Rolling 1:1

Eeriod

and initial

2Osec.

metacentric height

I

$

I

the and rn/sec. the including initial back of the. mass 2 axis is calcula-metacentric where As the very small, tions. [l,12]' where XFigures _in The relation T T -K xx K' xx g height = = = = = = = hydrodynamic square

between the rolling of a vessel is given 2

ir

(K

+ K')

period and by: [i] over of gyration the hydrodynamic gravity in meters longitudinal for all the vessel in meters

(p. 33)

symbol

\/g.i

rolling period in seconds;

(see fig. 1)

real transverse radius vessel in meters

radius of gyration of in meters

acceleration due to metacentric height in

mass about the

K,t will be used

+

radius of gyration of

the hydrodynainic mass

brackets see References

the

Kxxt

Kxxt

Benaming

Formaat

Auteursrecht orbchode, volgen3 de wt

Schaal - Gecontroleerd

Benaming

Formaat

A4

Rangschikmerk

The value of the hydrodynamic mass, dependent on the angle of heel, the maximum section coefficient, the speed of the vessel the breadth/draught ratio and the size and place of the bilge

keels, can only be determined by model tanktests. [3]

The transverse radius of gyration Kxt can be expressed in a percentage of the breadth of the vessel; the before mentioned formula can now be stated by:

T

YZ.B.Cr

c

2.Kxxt

f2

_Vg.GN

r B

where B = breadth of the vessel measured amidships, in.

met ers

C = rolling coefficient

r

The radius of gyration, consequently the rolling coefficient depends on the type of vessel, the form of the body, the division and grouping of the vessel, the fishing methods, the draught! depth ratio and the amount and place of the catch, ice (for preservation), freshwater and fuel.

Consequently it can be stated that if rolling coefficient and rolling period are known, the metacentric height can be determined fairly accurate.

The formula, however, is restricted by:

i >-0.20 meter [lo,llj

If i <0.20 w.>- O the formula of Wendel has to be used.

This formula will find no application due to the present stabilit

requirements.

3. Description of the vessel (see fig. 2)

The first serie

of

tests has been executed with a modern

sidetrawler, which came in service spring 1968.

Main particulars:

-length overall _LOA = 26.25 meters

length c.w.l. = 23.15 ' length p.p. = 23.35 moulded breadth 13 = 6.40 " depth amidships D = 3.10 draught forward (c.w.l) df = _1.95 draught after (c.w.1.) _da = _2.63

Auteursrecht voorbehouden volgens de wet Getekend Gezien Schaal Gecontroleerd

-4-OF SIDETRAWLER

mm 2 x 350 mm 26 x 450 mm

1OO mm

w.1.) dffi = 2.29 meters urne

= 164.16

m3 ght =

169.53

tons (metric) tre of buoyancy e, half

t (L,)

ient cient coefficient

four stroke main engine, developing

w. The engine drives, via a gearbox

ing of

2.94

: 1, a propeller with

Schaal Getekend Gecontroleerd Gezien Formaat

A4

Rangschikmerk I

FIG.2

Benaming

PROFILE

145. mm

24 x 450

mean draught (c. displacement vol displacement wei longitudinal cen in relation to

--angle of entranc

block coefficien prismatic coeffi waterline coeffi midship section

The vessel has a

540 b.h.p. at 750 r.p.

with a reduction gear

fixed pitch:

Auteursrecht voorbehouden volgens de wet

APP

FIP

1. wheelhouse/chart-r oom

5.

fish hold

2. galley/mess

6.

netstore

3. crew's quarter 7. fuel tanks

4.

engine room 8. freshwater tanks

LCB = -

0.342 w (1.46%)

1E =

31.50

CB =

0.480

C, =

_0.645

C. = 0.771 CM = 0,744

ea/disc area he vessel: V = 9 - 10 knots V = abt. ₄ beam trawling eriods D

= 2000

n P = 1,290 mm AE/AO

= 56 %

z

=4

hing periods vere measured by means of rtable "roll recorder't; at sea only with

recorder is manufactured by Muirhead D-993-B. This instrument has a gyroscope d its motion relative to the vessel is ly to a pen which registers the rolling per. The roll angle scale of the recorder

(25.4 mm) deflection; at its full extent s of heel. The paper speed can be varied. er is shown in fig. 1. The time factor is

in units of 20 seconds. The angle of roll, ted vertically. The 0-line, in this case the vessel heels, is difficult to

deter-at fact the rolling period T, is

deter-rolling time between two successive peaks o axis. 'Fo determine the relation between

the rolling period the _single period

gle is shown in the figure.

s been executed before the rolling tests e of gravity above the baseline belonging ndition. The relation between the inch-hts, and the initial metacentric height

y: Formaat

A4

Rangsch 1k me rk diameter pitch expanded blade ar number of blades

The maximum speed of t free running fishing fishing method

4.

Recording of rolhin In harbour the

ro

a "stopwatch" and a Po the roll recorder.

The portable roll and Company Ltd., type as a stable element an transferred mechanical angle on a strip of pa is 16 degrees per inch it registers 28 degree The recording pap indicated horizontally heel or list is indica the line around which mine at sea. Due to t mined by measuring th

on one side of the zer the rolling angle and is measured and the a

III HEELING TEST

A heeling test h to determine the centr to a certain loadingc nation, caused by wel of a vesesl is given b

Benaming

Auteursrecht voorbehouden volgens de wet Getekend Gezen Schaal Gecontroteerd

Benaming Formaat

A4

Rangschikrnerk

p.1

-. tg

where p = inclining weights in tons (1000 kg)

i = horizontal distance over which the weihts are

shifted in meters

= displacement in tons (1000 kg)

f= heeling angle of the vessel

(i'f

40)

The centre of gravity above the baseline is given by:

KG=KM- GM

where = metacentre above baseline (hydrostatic curves) = metacentric height above baseline (heeling test) A "pendulum" (usual method) and the "roll recorder" were used to measure the heeling angle Ø of the vessel. The results

were as follows (see fig.

3):

At a deflection of

40'

and 2° no

difference was found between the results of the pendulum method and roll recorder; at a deflection of 1020 ' a difference of 2cm

was found.

G.M heeling test: 0.70 m (mean value). One must be aware of the

fact that at the execution of a heeling test an error of

measure-ment can be made of + or - 2%.

Pable lA

Table lB

Table 1C

test No d

A

f

i

/D f/B î T0 Cr

m tons m m m -- - m sec.

-heeling t.et 1 2.27

i66.4o 0.83 3.36 2.64 0.85

_{0.13 0.71}

_6.03

_0.7

inclining weights (total) _{2.32 tons}

centre of gravity of weights above baseline

_{3.85 m}

horizontal distance over which the weights were

shifted

2.90 m

light weight of vessel

_150.96

tons (of 1000 kgs)

K of vessel in light condition : 2.63 meters

Auteursrecht voorbehouden volgens de wet Getekend G ezie n Schaal Gecontroleerd

Benam Ing

Fo rmaat

A4

R a n g sr h im e r k

FIG.3

HEELING TEST

wind force Sm/s

1 I - I

0.74

0.7

2-m

0.70

GMc

08

I

FIG. 4

0.84

0.82

KG/D

0.81

0.80

e

Ô0

0.85-1 -

_o-dg

s h

-

0.83-(_ o! L) IO

test with

booms

angle of heel Ø

heeling test

dw. in percentage of

registered

-pendulum-1, 'I

-roll

recorder-loading conditions

2b

I

.0! i J /0

light weight

2d

2e

o o

io

20°/o

50/0 _{10 0/0}

Schaal Gecon trotee rd Gezien Aurcurçrecht oorbchouden vogenç de wee Getekend

Benaming test rolling test rolling test rolling test rolling test rolling test No 2F 2E 2D 2C 213

light weight of vessel =

150.96

_{tons (including gear and}

spare parts)

100% fuel = _{20.77 tons}

100% ice (for preservation) = 6.00 tons

100% catch = 3.00 tons

The loading conditions are calculated including the content of the freshwatertank, oiltank for hydraulic system and the

lubricating oiltan.k. The number of persons on board, luggage, instrunients, provisions, etc. didn't change during the tests. Free surfaces have been avoided as far as possible.

For the division and place of weights on board see fig.

_5.

Explanatory notes for fig. 5:

fuel catch deadweight in % of light weight of the vessel I ice fre shwat er fuel in % of total capacity ice in % of total amount Formaat

A4

Rangschikmerk catch in % of total amount

IV ROLLING TESTS IN HARBOUR 1. Loading conditions

The radius of gyration has been determined dependent on the loadingcondition of the vessel.

Rolling tests have been executed with the vessel in the following conditions: Table 2 20.55 100.0 100 o 18.21 79.11 ₁₀₀ o 16.27 59.0 100 50

13.93

34.0

99 100 10.62 9.6 98 100

Aut ursrccht voorbehouden volgens de wet Getekend Gezien Schaal Gecontroleerd

I

8

see page 8

2f

U UUlIuUU

uuiuua

_UUu!UPlUUU

._.I i....

45

.4

.8

È

E

L

o

t

o

o'

U UUIT

UUUUUiUUUU

UIURUIIUUU

UuuurIUU

UUUiIUUUU

.r4UUUr'ui...

45.

I I I

0

45

00

450

Benaming Form aat Schaal Gecontroleerd

A4

-lo-As the trips of these fishing vessels (beam trawling) are mostly very short (5 - 6 days) the loadingconditions vary,

independent of the sailing time. For that reason the loading-conditions of the vessel are expressed in a percentage of light

weight,

The i/D ratio is constant (with the exception of test 2B) due to the general design of this vessel (see fig. 1ì). As a

result there were hardly differences found in the arms of static stability (see fig. 5).

Comparison of measurements with roll recorder and stopwatch The "free" rolling periods were measured in the harbour with a roll recorder and simultaneously with a stopwatch giving the possibility of comparing the results. The results proved that differences between roll recorder and stopwatch can be + or

- 0.2 seconds. It must be remarked that in harbour it is possible to make use of a fixed point, for instance a quay. At sea it can

be expected to make greater errors of measurement. Ralph Norrby

[6] notices: the error in. the measurement of T,, can be 5-10%.

Y'2 N

Free and forced rolling motions

In the harbour it has been checked whether differences in results can arise between "free" rolling and "forced" rolling.

(in smooth water)

Free rolling: The vessel is brought into a rolling motion by external forces (in this case by pulling a line connected to the mast).

The rolling periods are measured during the free-and damped motion of the vessel.

Forced rolling: The vessel is brought and kept Into a rolling motion by the same external forces. The rolling periods are measured during the forced motion

(mass is added constantly).

This particular test shows that the "forced" rolling periods are on an average 1.2% less than the "free" rolling periods.

Benaming

Formaat

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Rangschikmerk

Auteursrecht voorbehouden vogers de we Getekend Gez en

Benaming

amount of added mass (see fig. 6).

Influence of bilge keels

The Influence of the bilge keels on the rolling angle has been proved by tests at sea and in towing tanks [9]. The size of the bilge keels of fishing vessels (and the keel) are rather large compared to the dimensions of the vessel. Therefore it can be expected that the rolling period is influenced too. Exact values can not be given in this report, but will be a subject of

future study.

The influence of the waterdepth and the vicinity of a quay or shore on the rolling period

Results of modeltests (1959-1960) of the Technical

Universi-ty of Gteborg show that the influence of the waterdepth on the transverse radius of gyration (Kxxt) is small. []

Fig. 8 illustrates the results of modeltests of two vessels;

block coefficients 0.58 and 0.70. Fig. 7 illustrates the position of the fishing vessel (block coefficient 0.48) during the rolling tests.in the harbour of IJmuiden.

If we take into account this situation it will be clear that the modification of the radius of gyration will be small in most

cases.

Kxxq/Kxxt 1.01 for (; = 2.7)

where Kxxq = the transverse radius of gyration of the vessel including the hydrodyrzamic mass near a quay or shore and restrictive waterdepth (in meters) Kxxt = the transverse radius of gyration of the vessel

including the hydrodynamic mass in meters,

h = depth of the water in meters

dm = mean draught of the vessel in meters

However, the modification of the radius of gyration,snd

con..-quently the rolling coefficient, is not only influenced by the block coefficient and the waterdepth, but also by the breadth! draught ratio, the midship section coefficient, the form and

Auteursrccht voo,-bchouden volgens de wet Getekend Gezien I Rangschikrnerk

FIG.6

6.2 6.0 s

5.8

T02

A 5.6 I I

test No

2f

2e

FIG.7

wind force abt.4 rn/s

wave height 0.1-03m

-12-free rolling

forced rolling

n

---o

roll rec.

--free rolling

stopwatch

Jd

_Jc

d=draught vessel

h =depth of water

Benam Ing

Auteursrecht oorbchouden volgens dc wet

Schaal Getekend

i:

Gecontroleerd Geziert Fo rrnaat

A4

Rangschik me rk

FIG.8

o

lo

FIG.9

ROLLING TEST IN THE HARBOUR

ï:

-

_-

_{_.}

Ti__

_{jL aIim}

u

N=13

Benam ng

lo-01

-1

+ T=5755

b=Q3 s

N=13

T2

+ Formaat

A4

Ra ngsc h ik re e rk

3

4

h/dm

vessel h/d2.7

Auteursrechc voorbehouden volgens de wet Getekend 1t: Gezen

-14-the size of -14-the bilge keels and keel and -14-the construction of -14-the quay and/or slope of the shore. This subject will be studied further in connection with IV-4.

6.

Final results (tests in harbour)

The final results are shown in table 3 and fig. 10.

Table ₃

i) . 'xx

c

_A

where = nietacentric height corrected for free surfaces in meters

= metacentric height in meters

2

= specific gravity of internal liquid (fueltanics) in

ton s¡in3

I _{= transverse moment of a free surface in w4}

xx

= displacement in tons

Figure 10 shows that the rolling coefficient depends on the

loadingcondition of the vessel. As the roiling period does not vary strongly, the rolling coefficient Cr depends mainly on the metacentric height

Figure 11 illustrates the correlation between the rolling coefficient and the draught of the vessel. The curve shown in the

figure is not in agreement with the curve derived from the _formula

of Prof.Dr. H. Kato [2], caused by the fact that loadingconditions are expressed in draughts.

Benaming Formaat

A4

Ra ngsch 1k me rk

Fiure 10

testNo

d w tons f m f/B -T0 2 sec. Cr i w iT m

i/D

--c1

m 4-I E

L

2F 241 181.98 0.69 3.36

2.53 o.816

0.107

0.82 6.12

0.864

2E 2.39

178.44 0.71

3.36

2.53 0.816

0.111 O.1

6.00 0.843 2D 2.37

175.52 0.73

3.36

2.53 0.816

0.114 0.82 6.07

0.857

2C 2.33

171.99 0.77 3.37 2.53 o.[i6 0.120

_{0.83 5.94} 0.841

2B 2.29

166.99 0.81

3.37 2.57 0.829

0.127 0.77 5.92 0.810

Auteursrecht voorbchoudcn volgens de wet Getekend Gezien Schaal Gecontroleerd

I

,0.8

FIG. 10

_2f

0.8

0.82

0.80

0.82

0.80

0.78

0.76

2e

2d

2c

2b

62

6.0

5.8

Bertaming Formaat

A4

Ra ngsc h k me rk

TEST No

-

_í.

s_

T2

-m

ïc

in percentage

deadweight

of

light weight

I i i i i i i i i i i I i i I i I I I I J J I

200/o

10 0/0 Gecontroleerd Schaal

r

Gezien Autcursrecht voorbehouden voIgen de wet Getekend

I I (9 , I I LC) co

o

u t

-16-o

o

I I E

L

o

(n

o

c\J (n cJ

E

'f

Benaming Schaal Gecontroleerd Formaat

A4

Rangschikmerk Getekend Gezien

However, tor fishing vessels a loadingcondition as for instance "departure from fishing grounds" (full loadingcondition for other types of vessels) does not necessarily coincide with a maximum

draught.

Formula of prof.dr. H. Kato:

H2

Kxxt2

= f { CB I C + 1.10 CU (1 - CB) ( - 2.20) +

-

j B Cr = 2 . Kxxt/B

where B = breadth moulded in meters

Kxxt transverse radius of gyration in meters

CB = block coefficient

C = the upperdeck area coefficient

the effective depth, i.e. the depth moulded plus mean height of projected areas on profile of erections and deckhouses

mean draught

a coefcient depending on the type of vessel (tuna boats f = 0.2)

V THE INFLUENCE 0F THE POSITION OF THE BOOMS 0F A BEAN TRAWLER ON THE RADIUS 0F GYRATION

In the harbour tests have been done to check the influence of the position of the booms on the radius of gyration.

The following tests have been executed:

Vessel with the booms in vertical position (harbour-condition)

Vessel with the booms in a ₄₅ degrees angle to the horizon

(heading for fishing grounds)

Vessel with the booms in the crutches (harbour- and bad

weather-condition).

Figure 12 shows that the variation of the rolling coefficien is small. As these tests are executed with a small draught,

com-pare tables 3 and

4,

it will be expected that the influence under

normal loadingconditions will be smaller, in other words the in-fluence of the booms on the total mass of the vessel will be smal].

All the other tests, with the vessel free running, are

exe-cuted with the booms in a 45 degrees angle to the horizon.

Benamrng

t

Formaat

A4

Rangschikmerk H = d m = f =

Aut.ursrecht voorbehouden volgens dc wet Getekend Gezien Schaal Gecontroleerd

Benaming

7/I

in the crutches

0.83

Gecontroeerd

Cr

.82

.81

m.

.76

GMc

I' .74 Form aat

A4

Ra ngsch ik me rk

FIG.12

6.1-T0260

5.9-0.86

KG/D

0.84

TEST No

-18-booms:

vertical

450

Schaal

Autcursrecht voorbehouden votgens de wet Getekend

-r

Gezien

I

Table 4

VI ROLLING TESTS AT SEA 1. Loadingconditions

The rolling tests at sea are done with the vessel in the same loadingconditions as in the harbour (see table 3).

Te st

s:

Table 5A Table 5B

Corrections have been made for the fuelconsumption at sea.

2. Measurement of rolling periods at sea

As discussed already in II-4, the rolling periods are deter-mined by measuring the time between two successive peaks of the

rolling cycle on one side of the zero axis due to the fact that

the 0-line ja not constant.

Figure 13 shows that the 0-line of the free running vessel

varies by + or - a half degree. This is mainly caused by the

variations of windforces and the course alterations.

During fishing the variation

of'

the 0-line (see fig. 14) is

maximum + or - 3 degrees. Benarning Formaat

A4

Rangschikmerk Figure 12

test No.

d m

A

tons

f m

f/B

-T0 2

sec.

Cr

-ii

w ni

/D

--

w

-E 2A1 2.20 156.95 r.90 3.39 2.6j 0.852

o.i4i

0.7386.080.814

2A

2.20

156.95

0,90

3.39 2.63 o.848 0.141 O.7486.090.82l 2A3 2.20 156.95 0.903.39 2.61 0.342 0.141 0.768 5.94 o.8ii fishing sea harbour

'iA-1

4A-2 4A-3 4B

4E-1

4E-2

2C 2C 2C 2C 2F 2F

Auteursrecht voorbehouden volgens de wet Getekend Gezien Schaal Gecontroleerd free running sea 4

4D-1

4D-2 4F 4G-1 harbour 2C 2F 2F 2F 2F

o

z

z

z

D

Q::

w

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Gezien

Auteursrecht voorbehoLden volgens de wet

This is on account of the windforce, course corrections and the

mutual varying bottom friction resistance of the nets.

Statistical analysis of the rolling motion

The measured rolling periods were classified and collected into a histogram. The following characteristics were determined and calculated for the distributions:

b classified breadth in seconds

N = number of observations

= the mean value of the rolling period at sea

calcula-X'2N

ted by means of N observations in seconds

1V

x (arithmetical mean value) = ¿ x

Il

s = standard deviation in seconds

I

2 2

(x1 -( x.) ¡N

N-1

As the research in the first place is done to determine a

reasonable mean value, possible assymmetry positive as well as nega tive and strong accumulation of peaks around the centre will be left out of consideration (see figures 15 and 16).

The results proved that the mean value of the rolling period

is within the limits in 95 cases out of 100.

_[5]

Number of observations

From a number of tests it appeared that to determine a

reliable mean value for T at sea, belonging to a certain

load-ingcondition, one has to take at least 170 - 200 observations. In figure 17 the mean rolling period over an increasing

number of observations is plotted, viz. ,

T

=!cT

ø2 N

N _2sea

Beside that the mean rolling period over 10 observations has been plotted, viz.,:

T

=_!...T

(N=lo)

2 (10) 10 2sea

The diagram illustrates clearly that the mean value becomes

reasonable constant only after 170 observations. From the plotted

Te-2

(io) values itjs clear that errors can be made of + or - 13%.

Benaming

Formaat

A4

Rangschik me rk Auteursrecht voorbehouden volgens de wet Getekend Geziert

Benaming

f

-22-

0-0

I e!

/

I I i I I -1 +1 +2

+3 +4

+5 +6

TØ2N

sec.

-2

-1 I ₊₁

sec.

TØ2N

T2N= 5.7

s

1Ø2N= 6.3

s

b

=0.8s

s

=2.0

s N

₌₂₅₀

+4+5+6

Formaat

A4

Ra ngsch 1k merk

ri

I g N ¶

g

5

o

90

50

TEST 4

f

-5 -4

3

-TØ2

_se

FIG. 16

TEST

4g-1

-6-5-4-3

TØ2se

b

0.8s

s

=1.Os

N

=250

N ¶

_o

Auteursrcchc voorbehouden volgens dc wet Getekend Geilen Schaal Gecontr&eerd

Auteursrecbt

oor bohouden vulgenc dc wet

Sc haa I Getek end

-23-o

o

oJc'J

o

L'

Q

io t') Gecontroleerd Gexten Form aat Rang st h ik me rk

f)

z

Du

C

o

I-., D

>

L Q) u)

o

9-o

L Q) -o E C D Q) (f)

ci

\,ti-(1) (n c

'ti

-.

---.----.

r

t

-1I__Iz-I

II U

Z

('J ('J

I-j

I.-_--j

ill

1---I ___._o

O_

/

. -f

---a. °

----_tJ

---r

I --i'

o.-i

_,---tt---_o

eez4: DCJ

o

I

P

c; ('j

i i

's

t ¡ t s

r

i

Q

(D s

N

(5 IL D

f

Benaming

Vship

-24-V

= speed of

vessel

rn/s

c

= wave velocity

rn/s

Lw wave length

m

= wave direction angle

he wave direction with respect to the vessel vessel are caused by the waves met by the

has six degrees of freedom, three displace-r system and thdisplace-ree displace-rotations about these

re: surging swaying heaving pitching roil in and yawing

Waves: the irregularity of the sea has been the obstacle to its precise description. The sea is mostly described by idealized

wave types, such as the "trochoidal wave" which rarely exists

in nature. The waves can be assumed to be built up of a large number of regular waves of different height,. length and

direction. For deep water there is a theoretical relation between the wave length and wave period.

Formaat

A4

Rangschikmerk I

FIG. 18

5. The influence of t The motions of a vessel.

Ship motions: a ship

ment s in a rectangula

axes. These motions a

Auteursrecht voorbehouden volgens de wet Getekend Gezien Schaal Gecontroleerd

'1

.Y. LW

V _g

where T = wave period in seconds. Lw= wave length in meters.

g = acceleration due to gravity in rn/sec.2

The period of encounter TE depends on the wave direction

angle,4i.. The angle of roll depends on the ratio between P

F2 sea and TE.

A

= 180 ; TE = T). Resonance will occur if

is equal to

'r

. (See fig.

i8)

Z'2sea E

As the waves along the Dutch coast are very irregular the

formula of the trochoidal wave can not be used (Lw<

F---Therefore only the influence of the wave direction with respect to the rolling period of the vessel has been determined. Two tests are executed as follows: the course of the vessel was changed

perpendicular to the waves (,4= 1800). The wave period, the wave

length and the wave height were measured. The rolling motions

were now recorded with a speed of about

8.5

knots. After this,

the course was altered ₄₅ degrees to starboard; the rolling

motions vere recorded. These measurements were repeated till the vessel was back on its original course (perpendicular to the waves/head seas).

The results are given in table 6 and figures 19 and 20. It

is shown very clearly that in the "resonance area" T,, ¡T, = 1

1'2sea J1

and with beam seas

(/t=

90 ) the smallest divergence is found

compared to the rolling period measured in the harbour.

[4]

Benaming

Formaat

A4

Rangschik me rk Auteursrecht voorbehouden volgens de wet Getekend G 'zien

Benam Ing Form ai t

A4

Rangsch k nie rk

i

4-FIG. 20

00

_45°

900

_135°

_180°

0°

45°

900

135°

1800

wave direction angle

following seas

-26-2N

TEST No 4d-2

beam seas

head seas

T2(harbour)

.

.

=To

(resonance

area)

!?_Çharbour)

-

7-U)

z

cJ

6

5-7

U)

z

c\j

6-5

T2N =1qs

(resonance

area)

FIG.19

TEST No 4

Sc ha a I Gecontroleerd

I

Table 6

test Lj

(2C)

T

= 3 seconds

Lw = abt. 14 meters

wave height 0.35-0.40 w

windforce abt. 4.5 rn/sec.

Vship = abt. 8.5 kn. = 4.4 m/sec.Vship = abt. 8.5 kn. = 4.4 ni/sec.

1800

1350/2250

90° /2 7 0°

45°/315°

00

Auteursrecht voorbhoudcn vogens dc wct

T

N (sea)

5.5

5.9

6.1

6.2

Tf2

(harbour)

= 5.94 sec.

-27-Schaal Getekend

test 4D-2 (2F)

T = 3.3 seconds

Lw

abt. 17 meters

wave height 0.55-0.60 m

wiridforce abt. 5.5 in/sec.

180°

1350/2250

900/2700

450/3150

0°

Benaming Gecontroleerd

(harbour)

= 6.12 sec.

Fishing

The rolling periods measured while fishing deviate strongly

from the rolling periods measured in harbour. The number of

para-meters, which have to be taken into account compared with the free

running vessel, is increased. Besides the wave spectrum and the

wind, we have to consider the gear, the position of the booms,

the seabed condition, the net (hydrodynamic resistance/bottom

friction resistance) course corrections and tide

(intide/tide-ward).

The influence of the vessel's speed on the rolling

_w2tjons

The rolling motions of a vessel are also influenced by the

damping property of a vessel dependent on the speed through the

water. During fishing the rolling motions were registered

depen-dent on the speed of the vessel and the speed of the

gear over

the ground (o - 4 knots). Differences of a maximum of 0.3 seconds

of T,f

were measured.

1'2 sea

Formaat

A4

Gezien Rangschikmerk

N (sea)

5.5

5.7

5.9

6.i

6.2

-28--Free running measurements will be executed during the next series

of tests.

8.

Final results (tests at sea)

The final results are shown in the tables 7A and 78.

Table 7A (free running)

///see table 6

Table 78 (fishing) (booms horizontal)

VII THE CORRELATION BETWEEN THE ANGLE OP ROLL AND ROLLING PERIOD Tests were executed to study the correlation between the angle of roll (over and back) and the rolling period. The angle of roll was measured for each period.

Benaming Gecontreleerd Gezien orcnaat

A4

Rangschikmerk sea harbour -test no. cond. no. wind rn/sec. Vehip rn/sec. Lw at T sec.

A

T0

N sec. T02 sec. 4 2C

4.5

4.4

abt.

1k

3.0 ////d////1 594

4D-1 2F _5-7 4.6 abt. 18

3.4

1800 5.2 6.12 40-2 2F _5.5 4.4 abt. 17

3.3

_{///////J'i 6.12}

4F 2F 5-7 4,4 abt. 18

3.4

1200 5.7 6.12 4G-1 2F 5-7 4.2 abt. 18 3.4 35° 6.3

612

sea harbour test no. cond. no. wind rn/sec. Vship rn/sec. Lw at T sec,

A

'T0 N sec.

T0

sec.

kA-]. 2C

4.5

1.8 abt. 14 3.0 115°

5.4

5.94 4A-2 2C

4.5

_0.3 abt.

14

3.0 _115° 5.0 5.94 48 2C

4.5

0 abt. 14 3.0 1300

4.4

5.94

4E-1 2F

5.5

2.3 abt. 17 3.3 1300 .6 6.12 4E-2 2F

5.5

0.5

abt. 17 3.3 50° 5.9 6.12 Schaal Auceursrecht voorbehouden voIg.n de w. Getekend

FIG. 21

20

icr

Auteursrecht vnor&cnøudcn volgens dr wet

-29-TEST

4g-2

2d'

r'

--

-FIG. 22

TEST

4e-3

T2 (harbour)

free running

wind force 5-7 rn/s

Benarn ¡ng Getekend Gezien f is hi n g_

wind force 5-7 rn/s

Rangschikmerk I I I 0.5

_102N

0.5

1,5

T2sea

sec.

max. roll angle rn(over and back)

mean value of the largest third of

angles

Schaal Gecontroleerd

0.5

15

1

0.5

' T50

30-i

T2N

sec.

Fo rmaat

A4

-30

The mean value of the largest third of the angles within each group of periods (b = 0.3 sec.) was calculated ("significant angle of roll"). The maximum angle of roll in each group of periods was also measured. The results are plotted in fig. 21 and fig. 22 and are characteristic of all the measurements.

The figures show that the maximum angles of roll 0max occur in the area where the motions are frequent, i.e. around the

vessel's natural rolling period. The significant angle of roll is constant between + and - 1 second of T2

N (sea).

[8]

VIII CONCLUSION

1. General

The tests and calculations show that:

The distribution of the rolling period at sea accumulates around a mean value which shows no great deviation to the vessel's natural period of roll in smooth water.

The distribution of the rolling period shows no great

asymmetry.

When maximum angles occur, the vessel rolls in the vicinity of the natural rolling period.

k. To find a reasonable mean value, 170-200 measurements have to be taken.

5. Rolling periods measured during fishing, give unreliable values to determine the rolling coefficients.

2. Degree of accuracy

The following accuracy expressed in percentage has to be taken into account:

At a heeling test an error can be made of + or - 2% of i.

The reading error of the roll recorder amounts to + or - 0.6% of the real rolling period.

The error of measurement of the stopwatch compared with the

roll recorder is maximum + or _Ij% of T- (in harbour).

02

The difference between the rollïng period measured during "free" and "forced" rolling can amount to 1.2% of T02.

The size of the bilge keels will influence the rolling period (an exact percentage can not be given yet).

Benaming Gecontroleerd Gezien Formaat

A4

Rangchikmerk Schaal Auteurrecht voorbehouden voIgen de w.t Gecekend

The influence of the waterdepth and the vicinity of a quay or shore depends among other things on the ratio between the depth of water and the draught of the vessel..

(hid > 2.7 K z: 1%)

ni

The rolling motions are influenced by the speed of the vessel

(an exact percentage cannot be given yet).

Figure 23 shows the correlation between the breadth of the vessel, the rolling period, the rolling coefficient and the mata-centric height. The degree of accuracy of the formula can be read out directly from thenomcgram dependent of knowndata.

3.

Metacentric height and rolling period

Finally it can be stated that the metacentric height of a fishing vessel at sea under different conditions (loading and

weather) can be determined by measuring rolling periods, with an

accuracy of + or -12%; considering the following important points. The rolling periods may only be measured if the vessel is free

running.

Rolling motions have to be recorded by an instrument specially designed for this work.

At least 170-200 measurements have to be used for the calcula-tion of T12

N

Seanieasurements of rolling periods have to be taken with beam

seas (AL = 900) _{or in the resonance area (only in irregular}

waves).

Rolling coefficients must be known for at least four normal existing loading conditions of the vessel. These rolling coefficients must be determined and calculated in harbour.

The above mentioned accuracy of 12% is restricted to measurements done with windforce up to 5 Beaufort.

Closing remark. As the tests will be continued with other fishing vessels, the final results may deviate slightly from the results

obtained with this side trawler.

February,

₁₉₆₉

Benaming Gecontroleerd Gezien Formaat

A4

Rangchikmerk Schaal Auceurs,echt voorbehouden volgen de wet Getekend

12-

10-

8-

4-2

T_Ø2

,r.B.Cr

-

___

32-FIG. 23

GM-T2 NOMOGRAM

1.80

- 1.60

m

2.20

2.00

1.40

1.20

1.00

0.80

Benaming Formaat

A4

Rangschikmerk

Cr =0.80

Cr =0.75

0.60

C

_r

=0.70

0.40

0.20

Autcursrecht voorbehouden volgens de wet Getekend Gezien Schaal Gecontroleerd

s

14-DANCKWARDT, E.

1964

KATO, H.

1956

MÖCKEL, W.

1958

IX REFERENCES

Design part of:Henschke: Schiffbau-technisches Handbuch, Band 2 (Hand-book of Shipbuilding Technique) Approximate methods of calculating the period of roll of ships. Jouru.

SNAJ, Vol. ₈₉

MYERS, J.J., HOLM, C.H., McALLISTER, R.F.: Handbook of

1969

Ocean and underwater engineering.

Prepared under the auspices of North American Rockwell Corporation

Handbuch der Seefischerei Nordeuropas (Handbook of fishing vessels), Band XI,

Heft 5

NORRBY, R.A., ENGVALL, L.: Statistical analysis of the

1961* rolling motion of three coasters;

European Shipbuilding No. 4, Vol.

XII NORRBY, R.A.

1964

NORRBY, R.A.

1962

TRAUNG, J.O.

1957

VOSSERS, G.

1959

Stability problems of coastal vessels; International Shipbuilding Progress,

No. 121, Vol.

11,1964

The stability of coastal vessels. The Royal Institution of Naval Architects, Vol. 104, No. i

On the stability of fishing vessels. Shipbuilding and Shipping Record,

August 22 and September

19, 1957

Fundamentals of the behaviour of ships in waves; International Shipbuilding

Progress, No.

6, 1959

Theoretische scheepsbouw, deel 1 VRIJLANDT, W.

191*8 (Theoretical Shipbuilding)

[il] WENDEL, K. Rollschwingungen und

1940 (Rolling motions and arms of static

stability), Schiffbau, 1940

1953

Schiffbautechnische Gesellschaft

Hamburg: Erkentnisse und Erfahrungen auf dem Gebiete der Schiffstabilitat (Knowledge and experience of

stabili-ty)

Benaming

Formaat

A4

Rangschikmerk Auteursrecht voorbehoudeFi volgens dc wet Getekend Gezien

Schaal Gecontrolcerd

E 'J

[2

E J

H

j

5J

[6]

r

7]

E

8]

E J

[lo

.1