Safety of beam trawlers with a fastening net

TECHNISCHE HOGESCHOOL DELFT

AFDELING DER SC1-IEEPSBQIJw- EN SCHEEPVAARTKUNDE LABORATORIIJM VOOR SCHEEPSHVDROMECHANICA

SAFETY UF BhAM TRAWLERS WITH A "FASTENING" NET.

J.A.Korteweg and H.Vermeer

Reort no. 551-P

ma

1982

2nd internätiónai Conference on

The Stability of Ships and Ocean Vehicles (Stability '82) Tbkyo.,Japan october1982

Delft University of Technology Ship Hydromechanics Laboratory Mekelweg2

2628 CD DELFT

The Netherlands Phone 015 -786882

SAFETY OF BEAM TRAWLERS WITH A "FASTENING" NET

H.

VERMEE;R*

AND J, A.

KORTE,WEG**

*Neth. Directorate General of Shipp'ing and Maritime Affairs,

**Deift University 'of Technology

The. Netherlands .

Second International Conference on Stability of Ships and Ocean Vehicles, Tokyo, Oct.1982

ABSTRACT

The main theme of the first part of this paper is to outline the mathematical evaluation of the motions of a beam trawler and the tensile force in the warp, upon the occasion one of the beamtrawis becomes suddenly fastened in an abrupt manner on an obstruction on the seabed e.g. a wreck during the operation of trawling. The mathematical model has been developed for

the vessel in still water and two alter-natives have been investigated viz, with and without propeller thrust during the

fastening of the beamtrawl.

In the second part of this paper a review will be given of the tests with a model of a beam trawler, which have been

carried out at the Ship Hydromechanics Laboratory of the Delft University of Technology, Netherlands. The objective of

these tests is to verify the aforementioned mathematical model with results of syste-matic model tests. Testequipment, test-programme and procedures, which include

the measurement of all relevant parameters, are described.

In the last part of this paper the calculations according to the mathematical model are compared with the model test-results which is followed by a discussion of the found discrepancies and an analysis

of the trends observed. This analysis has revealed a number of preliminary

con-clusions relating to the stability of this type of vessel and the strength of fishing gear, which could well be of importance for both regulatory and design purposes. Finally this contribution is concluded with a few remarks with regard to the possible application of the findings of

the investigation in order to improve the safety of beamtrawlers.

SAFETY OF BEAM TRAWLERS WITH A "FASTENING" NET

H. VERMEER* AND J. A. K0RTEWEG**

*Neth. Directorate General of Shipping and Maritime Affairs,

**Delft University of Technology

The Netherlands N0MENCLATtRE K0, KOH, K0 (ton) K1, K1H, Kiv (ton) S (ton) W (ton)

m(tonsec2m)

I, I, (tonsec2m) Bc (tonm) x, y, z (m) a, b (m) v (msec1)

S VII - I b

tensile force in the

warp arid its resp.

components.

additional tensile force in the warp due

to fastening of a beam-trawl and its resp. components.

thrust.

resistance of ship and fishing gear.

ship's mass including added mass

ship's mass moment of inertia including added moment of iner-tia in the

resp.direc-tion.

restoring moment coefficient of the rolling motion. longitudinal, resp.

lateral and vertical transfer.

rolling angle and yawing angle.

tgc, in which X. is

defined in the text. distance from ship's centre line to point of application of warp pull.

vertical and horizon-tal distance from point of application of warp pull to centre of gravity. ship's advance speed.

t (sec,)

' (sec)

&L, V, k '(tonm ) (m) (m) (ton) N (H.P.) CO time. circle frequencies as defined in the text.

spring constant of the warp. elongation of the warp due to K1. initial metacéntric height. shipt s displacement ship's power. coefficient. INTRODUCTION

Beamtrawling is a common fishing method in the Netherlands and to a less extent in the neighbouring countries. This fishing method is characterized by the occurrence of excessive dynamic external forces acting upon the fishing gear.

The external moment for a highpowered beam trawler may under special circumstances endanger the ship's stability and lead to capsizal. Due to this phenomenon several fishing vessels have foundered eepecially during the sixties when the fishermen had no experience with the particular features of beamtrawling.

An investigation into these accidents revealed 'that two different dangerous situations can be distinguished:

(1) A beam trawler attempting to release the beamtrawl after a fastener by hau-ling with the warp running' over the fishing block, atthe end of the boom without using a sliphook as required. This case has been investigated in a quasi-static manner for a trawler in general and 'accordingly a proposal regarding stability criteria has been put forward. to IMCO

(Ref. 1).

(2') A beam trawler suddenly fastening in

an 'abrupt manner on an obstruction on the seabed e.g. a wreck during the operation of trawling followed by a violent rolling and yawing motion due to the impact load exerted by the fastened warp.

This case will be investigated more

thoroughly, taking into account the dyna-mics involved. This paper presents a

description' of this investigation by means of a mathematical model and extensive testing of a ship model In idealized tank-conditions.

MATHEMATICAL MODEL

2.1 Basic Assumptions Arid Development Of 'Mathematical Model

Prior to the se't up of the fundamental equations of the mathematical model it is useful to outline the basic assumptions.

(1) In order to avoid complication of the

pr6blem it Is assumed that the process of fastening of the beam trawl occurs in still water, I.e. the effects of waves, wind and current are not

considered. in this respect it should

82--be mentioned that generally a' fishing vessel stops fishing approximately at Beaufort 8. S'o the possible adverse effect of wind and waves should be borne in mind when interpreting the results of this Investigation.

In principle a fastener may occur when the beamtrawl is digging into a sand bank3 which gi'ves rise to a gradual increase of the pull in the warp (Ref.2'). However, in this investiga-tion ,abrupt, fastening of the beamtrawl e.g. hooking a wreck is assumed being the most critical case. This has the additional advantage of being less complicated in the mathematical sense. In the eivations of motion damping and hydrodynamic coupling terms are

ignored, which is justified, bearing in 'mind the time period of the forced'

oscillation.

(i) Within this' study no account is taken of the effect of a sudden "upcast" of the unfastened boom so it Is assumed that occurrence of this phenomenon Is prevented by suitable means.

Prior to the occurrence of a fastener the following equation applies:

0 (1)

When a fastener occurs the differential equations of motion for the x, y, z, and tv..

direction can be formulated using Fig.1 and are gIven in 'Ref.3.

V

0 t.o

KOH+K1H

Figi: Coordinate' system and forces 'acting upon a beam trawler during a fastener.

Using Fig..2 the pulling

force.

in the warp due to the fastener can be expressed as:.

k.M1=kfx_rp...(zrc)}cosx.

(z)

where it has been assumed that Hooke's law

is applicable. In Ref.3

it

is shori that

the stress-elongation curve for a (used) warping line is a straight line for K1-values occurring in practice..

Fig.2. Etóngotion of the warp.

2.2Simpliflcation And Evaluation Of Mathematical Model

In order to solve..the mathematical model, consisting of (1), (2) and

the

differential equations of motion, the

following operations are carried out:

The differential equations of motion

have been linearized.

Second order terms have been neglected.

The coupling term with z in the equation

for Ki' (2), has been

ignored, because the resulting heave motion as such is

tie gligible.

Using the boundary conditions:

bo,v, =o (3)

the mathematical model can be solved for the various degrees of freedom. The procedure of the solution is presented in Ref.3 and the most important results are as follows:

c_V

(SLflCV,1

_5tLZLr.

Er 2(to2_a4?) ' WI

/

x= vL_r

ç,; (5) 111=_.1 :

(LO fLnW,I

_a22

5LflCii

_-

_{t) (6)}

r '

c w,

_4

w2

I(

k(x_rp_,er'ç)=.

=

kV(LW22w5Lnw

_SirLu9(7)

with

)L (2+).i.2) 1

2i2j

112jI/2 (8)

and

2k

,

x

B,

+k r!...2Q6 I1'o, _v2

2.

Result of Numerical Computations

The results stated in the previous

sub-paragraph are valid for the particular

case that the propulsion machinery is

stopped when the vessel gets a fastener. It is also pos'ibIe

to

sol'vO the

mathe-matical model for the case'

-t = o, S = o (9)

The solution for this particular case Is given in the Annex of Ref.3, where sub-stitution of S = o yields the equations 1+

-

7

inclusIve.

In order to obtain an idea about the

difference between these

two methods a

calculation, example has been elaborated.

Table 1: Basic data for nunrical calculation

Parameter

Value

(tcnsec2/m)

31 .2

I

I,

iç

(tcnsec2 m)

(tonsec2 m)

(ton)

333, 31+70 3.5 k (toiv'm) 13.33

BQ()

(tonnm)

. 11+3.5 (0.1+7)

v

(ni/see)' ' 2

r

a

(m) (m) 9 3.5 -

0.2

'S

(ton)

8.5

0.2 0.-0 E oi. 0.2 0.4

T

0 30 20 110 0

Propulsion moohln.ry stopped - not stopp.d

2

2

Fig.3. Results of numerical calculations.

The basic data are listed in Table 1 and the results are plotted in Fig.3. From Fig.3 it can be concluded that in case the propulsion machinery is stopped there Is a reduction of 20% in terms of maximum heeling angle. Taking into account the significant time delay usual in practice to reduce the thrust it is proposed to consider only the most critical case i.e. "without human Intervention", which has the additional advantage of being less

complicated In application. _:_ t(sec) 3 4

- t(nec)

- t(sec)

çApproolmstlofl ocoodIfl9 - to fonreuto Ill) S.-'S. 5' 5' 5' "S

t (sec)

Propulsionmator. Shottdynomometer Tachometer Yawing gyro. 5 Rolling gyro.

6. Vertically adjustable weight.

Fig).. Equipment and instrumentation of model.

VerticalLy and horizontally adjustable weights. Adjustable attaching points tor tishing warps.

Cable connection to towing carriage. Acceleration meters.

Rotating steel plate tar electromagnetic connection with lowing carriage.

84-. MODEL EXPERIMENTS

.1 Test Facilities, Model And Instrumen-tation

The model experiments have been carried out in the experimental tank of the Ship Hydromechanics Laboratory of the Delft University of Technology in the Netherlands. The dimensions of this tank

are: length = 150 m width 1f.2 m, depth

of water 2.55 m. The carriage can travel with speeds up to 6m/sec.

The model was a 1 15 scale model

of the Dutch beam trawler IJM l-'+.

Partliculars of this vessel and the model are given in Table

2.

The model was

constructed of GRP and was fitted out with the following instruments and equipment

(see Fig.'i-):

- propulsion motor, propeller shaft and propeller;

rudder with locking device;

- yawing gyro (measurement of yawing

angle);

- rolling gyro (measurement of rolling

angle);

- a mast with a vertically adjustable

beam.

At the beam two horizontally

adjustable attaching points for the fishing warps with dynamometers for measurement of the tensile forces in the warps;

a second beam also vertically ad-justable along the mast with two horizontally adjustable weights (adjustment of metacentric height and moment of inertia);

a vertically adjustable weight on a screw spindle (adjustmentof meta-centric height);

Electric brake

'Wotersurface

Ton hbottom

Fig.5. Arrangement of modeL in towingtank.

Table 2: Particulars of ship and model

Hookinobor

Dynamométer Electromagnet

Hoo king bar

' Towincarrioge

__._._L

narnomeèr

ELeckmagnet

N

IjrrrI

accelera;tlon meters (measurement of linear acceleration in x, y and z direction of a coordinate system fixed to the ship);

- a small rotating steel plate on the

- stem -head for 'the electromagnetic

connection with the towing carriage; - bilge keels and' bulwark with freeing

ports.

Powersupply and control of propulsion motor were carried out from the towing carriage, which stayed close to the inodel.during the test. The measurements were transmitted by flexible cables to the towing carriage and recorded on UY-recorders and instru-mentation tape recorder.

3.2 Testarrangenient And Program

The arrangement of the model in the towing tank isshown iii Fig. 5. The model was connected by warps with two siiedgeswhich were pulled over the tankbottom. The tensile force in the warps was' supplied and ad-justed by an electrical brake at each warp. As soon, the model had travelled sOme

distance to adjust speed, propeller revo-lutions and tensile force' in the warps the port s1ege was caught by a 'bar on the SHh1 MODEl 1 : ₁₅ Ingth b.p. (m) 23.25 1,. 557 Breadth mided (rn)

6)40

0.1+27 tpth mided (m) 3.10 0.207 Draught fwrd ' (in) 1

.95

0 130

Draught aft (ni) 2.63 0.175

Vo]im Of dispIacçnEnt (ni3) i61+.i6 oc861+

Centre of buoyancy

forward of [/2 ' (m)

' 0.615 .0.01+1

tacentre above base (rn) 3'.335 0.222

1/2 angle of entrance

of (3IJL ' 31'.5° 31.5'

Block coefficient 0)4-8 o.'+

Prismatic coefficIent 0.61+5 0.61+5 Warp

Sheave (

Sledae

bottom of the towing tank. During this

fastener the angles of roll and yaw, the

tensile force

In the warps, and the 1ine

accelerations In x

y and' z directioxs were

recorded.

At the start of every run the model

was connected to the towing carriage by an

electromagnet. The speed.of the towing

carriage was adjusted to the required

speed of the vessel during fishing and

the number of revolutions of the propeller

motor was increased until the dynamometer

between model and carriage showed zero

force. Then the model was disconnected

from the carriage and sailed free on her

own. Some seconds later the port sledge

hit the bar on the tank bottom and a

fastener was initiated.

To investigate the conformity of the

results of the modeltests with the

mathe-matical model .it was expected that beside

rolling angle and tensile force in the

warp also x and y according to Fig.1

could be determined from the tests by

mathematical treatment of the linear

accelerations. Further a number of:runs

have been carried out simulating different

situations. The main parameters and the

corresponding quantative variations are

shOwn in,Table 3.

Mist tests have been carried out with

the propulsion motor not stopped. Some

however were carried out with a stopped

motor at the moment of fastening.. From

the results it appeared that the

differen-ces between both tests are small in the

order of less than 5%, which is within

accuracy limits.

Table 3: Maln paranters ahi their variatiOns

Values signed

) are average ialues

Preliminary Considerations And

Measurements

Prior tothe model tests in the

towing tank the following subjects were

considered.

(1) The tensile force In the fishing

warps. of a beam trawler of currnt

prac-tice and dimensions under normal

con-ditions at different ship speeds during

fishing was supplied by the Technical

86--C 3 .c E 10 . a 0 07 in

GM

Irn) 07 1.0 di(m)

F;g.6. _{mâx and} K1 _max 0% function of 1.

Table 1f:

Tensile force fishing warps at different

ship speeds

Research Department of the Netherlands

Insitute for Fishery Investigations

(see Table 1+).

(2) From calculations with the

mathematical model it was shown that

differences in mass and mass moment of

inertia of + 15% did hardly affect the

resulting forces in the fishing warps at

the fastening of a net, nor the rolling

angle or the x- and y- coordinates.

Therefore it was considered sufficient

to measure f1 and f

In the following

expressions and to rise for f, f

and f

standard values of respectively

2.0., 1.95 and 0.25.

Ship speed (nVsec.)

Tensile force in warp

Ko(t)

1.5

2.30

2.0

.

3.00

2.5

3.98

3.0

5.37

3.5

7.12

Parameter:

Variation (for ship):

4

()

0.O

0.55- 0.7- 0.85- Lo

v

(in)

1.5- 2.0- ,2.5- 3.0.- 3.5

(m)

7.00 - 8.00 - 9.00- 10.00

11.00

k

(t./m) .'

8 , i2 16

-C-)

0.25

0.275

0.3- 0.325 - 0.35

S v=i$ rn/s ' £0 caIcutated r 9.0 m . measured E 0.30

I

k. 12 t/m

!3o 120 0 30 a E 10 04 0.7 10 = f1 m (f;L)2 04 0.7 10

Fig.?. mØ Dad Kimax as fUnction of ok

= fi

m=f2m

2

= f1 rn (fB)

The results of the measurements Of'

f1, and f. depending on the GM are given

in Table-5'.

The coefficients were measured by roiling tests of the model in air and water.

(3)

For the fishing warps was .chosen

"Nichrorne Alloy Vt1 wire of 0.I4 mm diameter.

To vary the elasticity of the fishing warps springs with different characteris-tics were connected between the warps and the dynamometers at the adjustable beam.

Table 5: Results of IasurenEnt of f1 and f3

0 -,o.-.colcu toted o measured B 0.4 07 1.0 Ce,r..t.d , 0 0 0 0). 0.7 tO

.-ii(m)

Fig.B. _mox and K1 max as function of

In this way the elasticity of the warps. could be varied between spring constants of + and 20 ton/rn (full scale).

(1-) After fitting out the model with the required equipment and instruments as mentioned earlier it was shown that the required variation of GM could be

ob-tained by moving the adjustable weights.

.1f Results Of Model Experiments The model tests. showed in general well reproducable results with a maximum deviation of 2.50 11ax and a maximum deviation of 2.5 ton in K1 _a All results are calculated from the moe tests for ship size.

The calculation of x- and y- coor-dinates from the acceleration measurements turned out to be very laborious and did not give acceptable results'. Therefore it was decided to focus on a comparison

of max and Kimax for mathematical model

and model tests'.

During the model tests according, to Table 3 capsizing of the model did not occur. In order to find out at what

combination of parameters the vessel would capsize the parameters were altered in an unfavourabie fashion until capsize did occur. The combination of parameters, which lead to capsize are shown in Table 6. From this table it can be seen that only a very unfavourable combination of parameters values which lies beyond the conditions found in practice will lead to caps±za'i.

V 3.5 m/s r9.0.m £.O3O k. 12t/m (m) f1 0)40 i.0'+5 O)+85 0.55 1.152 0)+17 0.70 1.072 0.385 0.85 . .1.001 O)+1,7 1.00 .. 0.98+ 0)401 v2.5 m/s .-6catcutoted r 9.0 m o measured E03O k. 12t/m E 110

On the other hand it should be kept in mind that all tests were carried' out without wind,, waves or currents. In this way the

danger of capsize under unfavourable operational conditions could differ quite considerably from that during the model

tests.

Table 6: Canbinaticn of parameters at capsizal

During the model tests it was observed that in' some cases permanent elongation of the warp took place

(see Fig.15). In these cases _1max lagged behind the expéCtéd' values. There-fore Klmax has beOn corrected i

thee

cases in the shown' manner. These

corrected K1ma-value and also the original values are shown in 'Fig'.8 and 9.

(1) In Fig..6-8theresults are shoiin of the maximum rolling angle and the maximum tensile fbrc in the warp at different values of GM. The values of r,

E and k were kept constant, only the speed of the vessel has been varied: -,

1.5, 2.5, 3.5 in/sec respectively for-the

ship.

(2),In F1g,.9-1'1 the resilts are shown

of the maximum rolling angle and the maximum tensile iorcein' the warp at different fishing speeds. The va:Ls 'of r, E and k were kept constant,, only GM has

been varied as O.1'0, 0.70 and 1.00' in

respe.c.tively . .

(3)

In FIg. 12 the results are shown of the maximum rolling angle and, the maximum tensile forc9 in the warp 'at

different, values of the si'ng .constan k., The values of v, r,E and GM were kept

constant..

'(Ii-) In FIg.13 the results. are shown of the maximum rolling angle and the maximum tensile fOrce in the warp at different values of r.

The values of v, 6 , k nd 'GM were kept

constSit.. .

('5) In Fig.i+ the reults are shown of the maiimum roIling angle and the maximum tensile force in the warp at

different valüeas of 6.

The values of y, r, k and GM were kept

constant. .

88-£0

90

1 20 10 10 00 Gi .0.40 m r 9.0 m . 0.30 k. 12t/m A-calcuLated measured 2

v(rn/s)

v(m/s)

Fig9. _. rnox ,ad K1 max as function of' v £

(6) In Fig.15 the results are shown of the rolling angle and the tensile force In the warp as a function of time. In this case the warp showed a permanent elongation and a flattened top of the K1-curve. This

curve has been corrected In the Inicated way to obtain comparable results of K1,max

+. DISCUSSION AND ANALYSIS' 'OF RESULTS

+.1 Comparison Of Results Of Model

Experiments With Systematic Calculations

'(1)'Reviewing the Figures 6-11 It can be stated tha.t the conformity between' the

calculated' tensile forCe in the warp-from the mathematical model and those measured during the ñiodel tests is good. This refers to the cdnformlty betvieèn the general appearance and character of thO

curves "for calculated and measured 'forces as well as to 'the conformity of their values.' One exception 1oievei

_IS

found in FI'g.9 where the calculated and measured forces do no.t well agree. Some polnts,In this figure'had to,be corrected because' of 'permanent elongation of. the warp .so.that.in this way-the

measured values could be less reliable than usual.

(2) The conformity between the maximum rolling angles calculated from

the mathematical model and those measured during the model tet's is considerably less satisfactory. In all cases the mesured angles are much saller than the

calculate,d angles., Though thi is a reassuring result, efforts' have been devoted to find' out, the origin of this

dis'crepency.

Parameter (for ship). Value

GM v r k (m) (nVsec) (in) (t/m) -. '' ,, ,, 0.30 ' 3.5 10 0.35

10 g 30 E 20 10 3. 4

Fig.10. _max K1max as function ot v.

One of the causes of these differen-ces could be expected to be found in the assumptions' arid approximations of the mathematical model. However as some of

these will produce smaller rolling angles and others for instance the linear

restoring moment B.- underestimate the

maximum rolling aniethe'Iarge dis

crepancies can hardly be explained on this basis.

Another cause of. the forementioned discrepancies could have been the neglect in the mathematical model of the increase of the tensile force in the non-fastening warp. According to Ref.2 this force is

also increasing to a considOra'bi extent during a fastener. However the recordings of this force during the model tests did not show any sub,stantil,. increae of the

tensile forc.e in the non-fastening waip. So the mathematical model was in this respect exactly in accordance.with the model tests and gives no explanation

for the found discrepancies.

A third possibIlIty was the 'in-fluence of the bilge and bar keels of the model at dfferent speeds. These

in-fluences were not included in the mathe-matical model. Therefore som additional

tests with the model of the beam trawler have been carried out without warps, but with a small weight at: the end Of one

boom. The inclined model was towed by the towing carriage until the required speed was obtained by adjustment of the propeller

revolutions Then the small weight was dropped overboard and the successive rolling oscillations recorded. The differences between the. rolling angles at different and zero speeds were In the order of '5

- 15%

and are by no means

'40 9 30' 20 C £ 30 'C E 20 110 10 0 i:i .1.00 n' r 9.0 m C.O,30 k.12t/m __6_calcutated . measured a 2 y(rrVs)

Figli. IPma and K1 max, on function of v.

sufficient to give an explanation of the

found discrepancies..

(3)

Reviewing the Figures 12-1'4 it can 'be stated that the influence of the spring constant on the tensile force In the warp agrees well with the correspon-ding results of the calculations accorcorrespon-ding to the mathematIcal model. The différnces

In _max are of the same order of magni-tude as mentioned before.

9 1. I, ' 40 8calcuLated V. 25 rn/s. r .9.0 m E. 030 , measured 4aO,7O m H 20 0 0 9 K 0 10 4 9' 12 16 20

..-k(t/m)

C 30' 8 E 20 10 4 12 16 20 k(tim)

Fig.12. _{'9max and} K1_max as function at' k.

K, E 30 I dii=0.10.m r 9.0 rn E. 030 k 12t/m .,actcu1ated a measured

The influence of the length of the boom r is according to the model tests much more marked than according to the mathematical model. A rather pronounced minimum andmaxirnum can be noted at resp.

r = 8 rn and r = 10 in (see Fig.13). This phenomenon could also clearly be observed

during the model tests.

The influence of C.- whiCh refers to the.steepness of the warps during fishing -on the tensile force in the warp is very small. The influence ofLoncmax is only slightly greater. Also in this case from the model tests is about 50 - 60% of

max according to the rnathéniatical.rnodel.

(1+) Reviewing Fig,.15 where Ki and

have been presented as a function of time, it can be noted that K1 measured during the model tests takes some more time to reach its maximum than K1, calculated from the mathematical model. From analysis

of equation (15) it is found that this difference must have been caused by differences in the elasticity of the warp and further structural parts between mathematical model and ship model. This could be caused by bending of the boom and mast including some elasticity in the connection of the mast foot to the deck of the model of the beam trawler. During the tests some bending of the booms has been observed and this situation has been Improved by rigging wires from boom ends to stem head.

The great differences between _ma according to mathematical model and moel tests are stated here once more. Also a considerable time lag for .max can be observed.

90-S

j30

120 9

C

0

Fig1L. _Prnox and 1<i max as function of E.

+.2 Observations On Gear S'trength And Stability

Equation

(7)

does no,t offer the.

possibility to derive an anaiyti.cal *

expression for the maximum value of K1. However, application of the law of pre-servation of energy (Ref.3) leads to:

-

sin.

(Th)

WI

Substitution of (1:0) into

₍₇₎

gives:

K1;:

LVsi,t

₍₁₅₎

Consequently. the approximate value of the maximum value of K1, reads:

K

.,kv

1maic

j

(16)

From subsequent cajiculations it can be shown that equation (16) produces a value for the maximum value of K1 , which exceeds the correponding value of. K., according to equation

₍₇₎

by about 10% (see e.g. Fig.3). Taking into consideration that K0 has a value in the. order of 5 - 15% of Ki it is believed that this expression (16) provides an accurate basis for gear strength cali

culations. This result may also be taken Into account when considering the effect of fishing gear load on submarine pipe-lines. An outline of this problem is pre-sented in Ref.5.

Using equation +) it can easily be demonstrated that the, maximum heeling angle is represented by the expression:

10 e 1 8 9 10

.-r(m)

C 2 30 E

.20

8. 10 0 7 8 9 10 11

Fig.13. _mas and Kimax as function of r.

a 2.5 rn/s 8calculated r 9.0 m measured k. 12 t/m OTt .0.70 rn a .2.5 rn/s -8- calculated £.0.30 e measured k 12 f/rn 40 _dT-i.o.lom E₃₀ I 20

ti;i o0:0 m v 3.5 rn/s C.. 0.30

,50. _r.9.Om k 1i2 t/m

Fig15. 'P and K1, as function of time.

Sm G2(l

₇₎

WI

This relation has .been.iised for systematic calculations, which revealed that for an arbitrary constant value of Qmax approximate-ly the following relation applies:

Coa.cf ion of K

'

.0.t.ot)

Where the subscript o refers to an arbitrary standard condition. Further ignoring the frictional resistance of the beanitrawls

the following approximate expression is valid:

N. fv N0

_lovI

- t(s).

(18)

From equations (18) and

₍₁₉₎

it can be derived that the initial metacentric height meets the following relation with the

ship's power:

This theoretical result should be modified taking into account model test results and full scale measurements. From model test results it can be shown that the exponent of the ratio

v/v0

of equation (18) is

approximately equal to

1.5,

which has been derived from Ref.LI. (see e.g. Fig.6-8). Likewise it can be shown from full scale measurements (Ref.6) that the exponent of the ratio

_v/v0

of equation (19) is

approximately equal to

_1.5.

For this pur-pose it has been assumed that an increase

of ship's power is: consumed for 50% by an increase in ship's fIshing speed and for 50% by an increase of the weight of the fishing gear, which is conform the existing practice. From these modifications

it can be concluded that the initial meta-centric height for the same

_nax

is

approxithately directly proportional to the ship's power in the range of actual fishing speeds i.e.:

GM_ N

- N0

(21) GM0

This basic concep.t of adaption of stability requirements to excessive propulsive power has been introduced in the national. legislation for application to beam

traw-lers.

With regard to the above mentioned standard condition the following ob-servations may be made:

According to the model experimental results and subsequent numerical calculations is _Qmax approximately independent of , k and r within the range of practical applications. According to the model experimental. results is rnax approximately propor-tional to v1', whereas the theory preducts a linear relationship. According to subsequent numerIcal calculations is _max approximately proportional to and both according to the model experimental results and subsequent numerical calculations is _ax approximately proportional to GM'3

It shou]d' be noted that these observations can be reflected in the following basic expression:

(19)

.

c=

C'2113

(22)

Taking into accouy that N is approximately proportional to v 2 (ref.6.) equation (22)

can be rewiitten as:

This relationship does actually give evidence that the standard condition,re-presented by the ship's power standard, can be expressed as a measure of the restoring moment., which is not

an

unexpec-ted result.

_fN\a'

(20)

_{N0 = C0}

_{. GM}

5.

CONCLUSIONS,

1.. Simulating. ,a fastener of a beam

trawler by model experiments is a feasible option, provided due attention is paid to the performance procedures.

The, analytical solutioO of the simplified mathematical model produces sufficient accurate results for further analysis and drafting.of regulatory re-quirements bearing in mind the observed. discrepancies.

The maximum pulling force in the warp due to an abrupt fastener can be approximately estimated by means of equation (1.2), providing a basis for the assessment of damage to asubmarine

pipe.-line.

-i. The maximum heeling angle due to fastening of one of the bearntrawls can be approximately estimated by means of equation (10), using a reduction fa'c.tor

of about 0.6. .

I has been dernontraited that the initial metacentric height is approximate-ly directapproximate-ly proportional to the ship's pOwer assuming .a cOnstant maximum heeling angle, whereas for the reference value there Is an indication that this standard

Condition can be dbscrlbed by the restoring moment coefficient.

The phenomenon of afastener, which has been investigated.for a beam trawler, can be extexded to other types

of fishing vessels although this repre-sents a substantial less Critical condition from the stability point of view because the nB-ratio is reduced to

less than one third of the value for a beam trawler.

92-6.

ACKNOWLEDGEMENT

The authors are very much inde1te4 to the Technical ResearchDepartment of the Netherlands Institute for Fishery

Investigations for Its kind eocperatlon and for the provision of the marr. valuable results of full scale measurements..

The valuable assistance of Mr.A.Goe-man in producing the graphs and of Mrs.

M..J.Beemsterboer in ty.ping the manuscri.pt

Is gratefully acknowledged.

REFERENCES

U.S.S.R., submission to I.M.C.O, "Effect of Fishing Gear on Stability of Fishing Vessels", I.M.C.O.paper PFV/276,

1979

Pinkster,J.A. "Invloed van Vis-niethode en Vistuig op de Veiligheid van

Boomkorkotters" (in Dutch), Master Thesis Techn.Univ.Delft, Oct. 1q70

Vermeer,J-. , "Note on the Safety

of Beam Trawlers.",. International Ship-building Progrss, Vol 22, No 2+, Oct l9'7'

Kbrteweg,J.A., "De Bewegingen van een Boonikorkotter bij het vastlopen van een visnet" (in Dutch), Delft University of TOchnology, Ship Hydromechanics Labora-tory Report N.o.1f65-M, June 1978

. MoshagOn,H. and TTjelden,S.P.,

"Fishing Gear Loads and Effects. on Sub-marine Pipelines", .Proceedips Offshore Tecitiology Conference, OTC 3782, Houston,

1980

6. Koldewijn,J.Th. and Mulder,A..A..J.,

"S tabi liteitseisen. voor Boomkorkotters

-Toetsing aan de.'huldige Risen en Ont-wikkelIng van een Aiternatief" (in Dutch), Report No.75-0-i- of the Technical Research. Department of the Netherlands In3tltute for Fishery Investigations,

1975