Studies on stability of fishing vessels on a wave crest

ON STABILITY OF FISHING VESSELS

ON A WAVE CREST

by

N.B. Sevast'yanov and Yu. I. Nechayev

as published in

"THE PROCEEDINGS OF THE KALININGRAD TECHNICAL INSTITUTE

OF THE FISHERIES INDUSTRY AND MANAGEMENT"

Vols. XVI & XVIII

and

"TRANSACTIONS OF THE REGISTER OF THE USSR"

1965 - Vols.

i & Z

TRANSLATION

from the Russian

prepared, by special permission, for the

International Maritime Consultative Organization

IMCO

Panel of Experte on Stability of Fishing Vessels

and published by the

The Department of Pisherie3 of Canada is grateful to Dr. Sevast'yanov, Senior Lecturer in naval architecture at

the Kaliningrad Institute of Pisheries and Russian delegate on the Panel. of Experts on Pishing Vessel Stability of IMCO who made the arrangements for these texts to be available to

all members of tha international panel.

Sincere thanks are also extended to Mr. V. Nadeinaki,

Head of the Ship Construction Section of the InterGoverninental Maritime Consultative Organization in London who kindly

coordinated ali activities that made this translation possible. These studies were efficiently translated by the

Foreign Language Division, Bureau for Translations, Department of the Secretary of State of Canada.

Jean Fréchet, Chief, Fishing Operations Branch,

Title Pare

Stability of' a vessel travelling on cairn water and an accompanying wave.

Ostoychivost' sudna pri khode na tikhoy vode i na poputnoy voine.

Dr. N.B. Sevast'yanov Concerning the influence of speed on the

stability of a vessel.

O vliyanii skorosii na ostoychivost' sudna. Yu. Nechayev

Changes in stability in relation to trim on accompanying waves.

Izmeneniye ostoychivosti na poputnorn voinenii y zavisimosti ot differenta.

Yu. I. iTechayev

Determination of righting arms for a vessel riding

on a wave crest.

55-68

Opredeleniye p lech ostoychivosti pri dvizhenii sudna na poputnom volnenii.

Yu. I. Nechayev

An approximate method of calculating the stability of' a vessel moving on the crest of'

accompanying waves.

69-79

Priblizhennyy sposob rascheta ostoychivosti sudna pri dvizhenii na vershine poputnoy volny.

Yu. I. Nechayev

l-21

22-38

by N.B. Sevast'yanov

Staiecerìt of problem and analysis of methodology of experiment Statement of problem

The objective evaluation of the stability of many types of commercial fishin?: boats can hardly be carried out with the usual methods used for evaluating ship stability. The reason for this is

the small size of fishing vessels; even under conditions of slight wave actions in the sea the length of the waves is commensurate with

the ength of the vessel and the vertical measurements of the waves are commensurate with its height and exceed several times the part above the water. As a result the actual waterline, outlining the

subrerged art of the vessel, cannot, even in rough approximation, be considered as level and it changes substantially in time.

Por large ships such significant changes in the plane of the waterline occur only in rare circumstances, while for commercial vessels of the open sea (trawlers, seiners, whale boats, tunny fish

boats, e-te.) for practical puroses such conditions continuously accompany their normal use. The obviously important influence of the deformity of the water surface on stability has forced individual forei]1 researchers to analyse their problem. (l,2,3,L,5,6,?).

Obviously its full analysis is made more difficult by the continuously changing character of the movement of

vessels on the wavy sea. Therefore, in the first instance, research is confined to the simple chance occurrence when the vessel ioves evenly and at right angles to the running

wave. In this instance the shape of the actual waterline, although not level, is unchanged in time when rolling of the ship is absent and movement becomes smooth (in the system of coordinates, related to the ship) . The overwhelming majority of solutions of this event were obtained by purely statistical methods: as a basic clearly formulated assumption can be taken the possibility of disregarding dynamic pressure in the waves, and, in connection with this, that the pressure on any given point of the body can be defined only as hydrostatic, proportional to the submerged depth of this point under the

wave profile of the free surface. This method is fully explained in the recent works of Prof. S.N. Blagoveschensk (1,2), used

as a base for the "stability norms" of the Register of the USSR (1959), as well as in the general works of E. Upahi (6).

The basic results obtained by this method lead to the following:

Disturbances of the water surface seriously affect the characteristic of stability.

The worst situation is when the height of the wave is placed on the middle of the ship, when the maximum ordinate of

Read's diagram may be significantly reduced.

The most unpleasant waves are those of a length

0,75 L<X<1,25 L, ₍₁₎

when 1 length of ship.

With other lengths of waves their influence diminishes, but, in all events this influence is greater the greater the steepness of the waves, that is, the relationship of the height of the waves 2rand length?L

Attempts at experimental verification of the results obtained by means of comparison of restored momentum of ehips

"statically" placed on the summit of the wave with experimental measuring of the movement of the model on an accompanying

wave were undertaken in the test basin of the Leningrad Ship Institute. These attempts were not crowned with success since it was possible to fix only a few points at small angles of heeling. Considering the reasons for the failure as technical, the authors of the report suggested that it would be possible to obtain a direct comparison of the experimental data with

the calculations of the statistical method with a better setting up of the experiment.

The basic factors which has previously not been considered proved to be:

The presence in the ship of the speed of movement.

The inevitable change of the relative movement of the ship and the profile of the wave when heeling occurred.

Let us study these factors more carefully.

A. The function of the speed of movement. In order to accomplish smooth movement of the ship or the model on the profile of an accompanying wave, it is necessary to impart to the ship a speed equal to that of the movement of the waves. Otherwise there would be a point, where the ship while passing or remaining behind the profiles of the waves, movement would inevitably be accompanied by rocking and the characteristics of stability would not remain only a function of the shape of the waves but would also depend on the time,

may apply fully to the simplest situation when

v-c (2)

when

v speed of vessel

c speed of wave spread

Assuming the wave to be cylindrical, sine-shaped, with an unlimited length, we have from wave theory

23tc2

g'

where

length of wave

g= acceleration of the forces of gravity.

If we introduce cv we obtain that, with a given speed of the ship, there may only be one relationship between the length of the wave, static in relationship to the ship, and the length of the ship, namely

X 2ivv2

- =

= 2-tFr2,

L gL

where

Fr = Froude's figure

Let us assume in conformity with (1) that the position of the ship on a wave

of?O.75

does not represent a danger; one has to admit that a smooth movement of the vessel on an

accOflJ)aflyiflg wave with a dangerfor its stability may only

occur in vessels capable of developing speed of a Froude figure:

that is

Fr>

O.3Li.6

1 I 1 /:0,75

The relationship = 1 requires a speed with a Froude

figure Fr'== =0,4. (6)

Table 1 shows the characteristic maximum Froude figures of commercial fishing vessels. It has to be borne in mind that the speeds quoted in the table refer to experimental conditions on a measured mile on calm water and not at full water

displacement.

Table i Characteristics of Typical Commercial Vessels

Notes: i. Characteristics quoted from handbook (Ls),

2. The maximum lengths of ships are used in these quotations.

From the data in the table it follows that for vessels operating in the open sea, only the whale boats and seiners have the speed sufficient to move with accompanying waves of dangerous sizes, without staying behind. The entire group of trawlers have a Proude figure which makes smooth travel on a large

G)Q)

'Or

r-4 _mir, ' ' c _{'> CI)} 't i-IP-i Q)+' bD (1)

0 '

Q) O O O P-i -i -P C CE1 4r bO( Q) _P-i P-i ObD CI)

o

i Whale Boat 63,6 41+00 _{17,4 0,36} 1,25 2 Trawler BNRT _84,7 2000 _{13,0 0,23} 3,0 3 Fishing Trawler 57,8 1100 12,3 0,27 2,18 1+ Fishing Trawler _60,9 800 11,8 0,25 _2,5+

5 Medium Fishing Trawler SRT-R 0,5 650 11,0 _0,25 2,51+

6 Medium Fishing Trawler SRT-R-400 L1J,5 400 10,0 0,25 2,51+

7 Medium Fishing Trawler SRT-300 39,2 300 _9,5 0,25 2,54

8 Fishing Seiner RS 300 25,0 300 10,0 _0,33 1,46

9 Medium Fishing Trawler SRS-150 25,3

150

9,0 0,30 _1,77

10 Small Seiner MRS-SO 18,8 80 _8,3 0,32 _1,55

11 Fishing Boat RB-l50 26,1+

₁₅₀

9,0 _{0,29 1,90}

12 Crab Fishing Boat 14,8 20 6,2 _0,27 2,18

Froude figure = 0.25, a position on the peak of a wave on the middle simultaneously corresponds to the position of the

neighboring waves on the 2nd and 18th theoretical ribs,

These considerations do not exclude the dangerous

situations of any commercial vessels on the crest of a large accompanying wave or an oncoming wave, however, the length of

sojourn of a vessel here also depends on the Froude figure. Statistical calculations in all these circumstances show that when the ship is situated in the "sole" of the wave its

stability becomes greater than on calm water. Therefore, with the movement of the profile of the wave along the side of the

ship, known periodic changes in the characteristic of

stability may be assumed: from the increased stability in the "sole" to the reduced stability on the "crest" to a roughly "neutral" condition on the incline. Let us take for a rough evaluation the following conditions:

a) As the "dangerous" time we will take the fourth apparent period of the waves

X I A

MaW

cv

i_: C

Considering that the true period of the wave is

=

?- _O,8V s and that V

=Fr

_C we obtain A

' 1Fr

i L

Se

b) Let us take

\

L,

Then (7)

on

4

l-FrV2n

The dangerous periods for the vessel of Table i are worked out in Table 2 according to formula (7), as well as the approximate periods of the rocking of the ship Co with a specified initial

value of the metacentric height of h0 =

0.61+ in.

Obviously, the reiationshìp does not

unilaterally indicate a point of danger of overturning, it may also be viewed only as one of the identifiable neutral parameters. However, the fact that there is a place of sharp difference

(twice and Lore) between the valuelfor the groups of medium and large trawlers and the groups of seiners, motorboats and

whaleboats is characteristic.

Table 2.

Coniparison 01' "dangerous" time wth the normal neriod of the natural rocking of the sh

ia1 Type of Ve ssei

1Froude ¿igure Wave Period

'Lsec

Width B meterto O ,BB toi ceic - ton sec

-

to

i Whale Boat

0,36

6,38

9,5

9,5

i6,

1,68

2 Trawler BNRT

0,23

7,36

14,0

114,0 14,32

0,31

3 Fishing Trawler

0,27

6,07

9,5

9,5

14,68 0,1+9

14 Fishing Trawler ° 2,

6,24

9,0

9,0

4,i4

0,46

5

SliT-H

0,25

7,11

8,8

8,8

f4,72

0,51+ 6

SRTR-400

O25

5,27

7,6

7,6

3,50

0,/46 7

GRT-300

0,25

5,01

7,3

7,3

3,32

o,1+6 8

RS-300

0,33

14,00

6,2

6,2

5,72

0,92

9

SRS-150

0,30

5,03

5,6

,6

5,03

0,90

10 I'IRS-80

0,32

3,146

4,8

14,8

4,34

_0,90

il

RB-150

0,29

4,10

5,5

5,5

3,74

0,68 12 Crab Boat

0,27

3,08

3,0

3,0

2,414.

0,81

13

'Dory'

0,36

2,38

2,7

2,7

5,95

2,20

It is not just chance that the majority of accidents

connected with the loss of stability occur with fishing vessels having a sufficiently high Froude figure. Even on incomplete

data, for the last ten years ten lossess can be quoted: Seiner no. 707 (RS-300) near the Kolsk Peninsula; Seiner type B Ch S ("Zarya" in the Caspian Sea); NRT-62 and MRT-171+ in the Baltic; whaleboat "Simbra" (Antarctic); several

American tunny clippers (Pacific Ocean).

We note in passing that the relationshiptmay be

given the following shape using equation (7): i

l.

4 _o

_1-FrV

or

Liz0

I

B B

_1-Fr1I

(8)

From this can be seen that lengthening a vessel and

increasing its metracentric height h0 increases the parameterE The analysed geometrical and kinetic relationships arising out of the presence of the speed of movement, emphasize the

importance of considering the Froude figure when evaluating the stability of small ships on the open sea. Obviously, the

evaluation of the degree of safety of a ship should be carried out in connection with the Proude figure, corresponding to the Thnaximum speed of movement. However, the function of speed is

not limited by this. As is obvious from the precedings, the question of stability of vessels on an accompanying wave has a practical realistic importance only with a sufficiently high Proude figure. Under these circumstances it is not permissible

to deal with a natural wave which lifts the vessel on its way.

It can be confirmed that the theoretical determination of the

effects of the wave profile and the fields of.pressure from the

impact of a natural or accompanying wave is at present impossible.

This is particularly true for commercial vessels with their short

lengths.

It is only clear that the dynamics of the effect of

movement is such that it can hardly be possible to disregard it

when deterrniningthe recuperative momentum while moving on

calm water as well as on an accompanying wave.

_{Therefore an}

experiment must be recognized as the only means of a qualitative

evaluation, and only after gathering sufficient experimental data

is it póssible to depend on the development of calculation methods.

B.

Changes in the character of movement when heeling.

_The

specific difficulty of the experiment is the disruption of the

symmetry of the environment when heeling..

_{The movement of the}

vessel makes the task three dimensional, but movement is Interrupted

since even with movement on calm water with sufficiently large

Froude figures the appearance of supplementary recuperative,

differential, and turning momentum is possible as well

as

lifting arid lateral forces and additional drag.

For this reason the modeling of heeling

_{on the movement of}

the ship requires the accomplishment of all 6 stages of

_freedom,

that is the conducting of selfpropelled trials. In this the

rnovement of the model will essentially depend on the dynamics

of the application of the internal heeling momentum..

_Movement

on a wave will make the picture more difficult.

_{In particular,}

with an unexpected heeling, one can expect in several

_situations

bolster to the wave as apparently occurred in the event of the loss of MRT-62.

However, the lack of understanding and the difficulty of the task compel us to study it to begin with in a simplified situation. Therefore we formulate certain assumptions:

The vessel is controllable; the turning momentum produced by the heeling can be compensated for by turning of the rudder. The continuing movement along the axis of the vessel (the course) is maintained.

The momentum of heeling is close to static, that is, it is infinitely slow.

Changes in resistance with variations of heeling, settling, and longitudinal trim are compensated for by changing the thrust of the propellor so that the speed of movement in the direction of the longitudinal axis of the vessel is maintained.

Within the indicated assumption it is possible to create the effects of placing the model in the four free positions: heeling, trim, floating and drifting.

In the experiments referred to above (1,2,3) the models were deprived of the freedom of drift which should lead to the disturbance of the natural conditions of balance. This

circumstance was not discussed in the accounts of the experiments, and apparently not considered.

Let us study the equilibrium of a model capable of moving in the three steps of freedom (Figure 1). The joint with the axis F permits the model to heel freely, axis ITN' permits the

free trim of the model, parallels KK1 ensure free floating and immersion of the model. The angle of drift is established

the projection of the equivalent forces on the part of the waters R on the surface of the frame will not be vertical and

the point of application C1 will not coincide with the centre of force Cl, which has been found to be the centre of gravity of the submerged volume.

The equation of equilibrium within a system of

coordinates will be:

D+R =0,

R+R=0,

We solve the last equation by means of the first two: D(g

-)+MKp+R(-Ç)=O.

In the normal system of ship coordinates

1=zsine+ç.ose,

=zcoseysine,

Then

D(zgsiflO_y1COS8csunl0)+Micp+

+R1[(z )osey sin

B]=O.

In equation

₍₉₎

the first number is analagous with the statistically established momentum. The difference consists in that the coordinates of the centre of the bulk of a non-moving ship at the given angle of heeling and of the surface prove to be functions of the shape of the

surroundings and of the main measurements of the vessel, when as with movement:

y1

=f (L, B, T, t. 12,...,

, r, u, y, g, X) and

z =f2(L, B, T, I, 12, . . ., ,, r, u, y, g, X),

when

l, 12 - is the aggregate of the geometrical measurements determining the shape of the ship.

- is the angle of drift

7,r-

is the length and half the height of the accornoanying

wave.

'V - kinetic coefficient of the viscosity of the water.

Prom this we get

L .B 1 r X y vL

¡L B

1

r

X y

We summon the first rnern'oer of equation (9) which establishes

the momentum while moving:

MDÚ'

COSO±Z SinOZgSiflO).

lt io also possible to introduce the concept of the ar:: of stability while movin.

tv=yCOSe+ZcSiIIHZgSiI1e.

(12)

The statistical methods of calculation, developed in the works (l,2,,6,) are directed to the study searching for

M orlz,e under the vague assumption that in the right half of the equation (10) the determining parameters - aid

are permissible, and that the angle of driftQ

As is shown above, disregard of the Froude figure is not

permissible even from the purely kinetic point of view. _Disregard of the Reynold figure, it seems, is permissible with low drift

angles and absence of eels, typical of fishing vessels, since the tangential pressure with continuing flowing around the ship can only act to a small extent on the lateral momentum, and the points of breaking awa:;r of whirling are fixed by the sharp edge of the keel and its tail.

The third member in equation is the. su:ple:nentary

exclusive of natural drift. Insofar as this deficiency was not -taken into account in the trials of the accomplished

experiments, its unknown quantity was automatically included in the experimentally determined value of the recuperative

momentum which made the results of the experiment non-comparable with the results of the calculations and failed to meet the

requirements of the task which had been set.

Certainly, in nature, the event of heeling quickly calls forth the appearance of lateral hydrodynamic forces. Under the influence of this force the ship obtains lateral

speed, hich in its turn changes the angle of heeling and the lateral force. With a slow change in heeling one can dispense with the forces of inertia and one can consider that this

process will continue as long as the cons.tant speed of drift and constant heeling does not stop. The speed vector resulting from this, a component of the speed of movement in direction DP and of lateral speed, should form with DP an angle of

drift0 with which lateral force disappears. The movement of the ship becomes level and straight lined. If at the beginning the vessel travelled on a course perpendicular to the front of the waves, then even no DP will maintain thia direction and the vector of the resulting speed will be guided under the angle So°-p,0 to the front of the waves.

Figure 2.

During smooth movement the heeling momentum is balanced by the recuperative, and will be distinguished from the

recuperative momentum on the stand on account of the

hydrostatic as well as the hydrodynamic composite. Further-more, the volume of the submerged part of the ship will not be

equal to the water displacement of a standing ship. Therefore equal volume banking, lying at the base of the search for the recuperative momentum of the statistical method appears to be an arbitrary procedure, the acceptance of which in certain instances must be demonstrated.

Separate particular instances are possible when the lateral force and the angle of drift will be known to equal

zero. As an example may serve gyrating bodies which sustain the * symmetry of the submerged part at any given angle of heeling,

if their axis of inclination coincides with the axis of turning of the originating force. In those events the

suspension of the model in the three degrees of freedom seems appropriate for the experiment. Ilowever for realistic ship

disregard of the force of drift is a possible source of errors. Applying the conclusions to the foregoing, it is possible to formulate a simplified problem concerning the stability of a vessel moving through calm waters and with an accompanying wave: to determine the value of the recuperating momentum with free

smooth movement on two sizes of waves of differing height

from

i ()

. The necessary and sufficient

conditions of smooth movement appear to be:

The uniformity of the spreading speed of the waves and the projection of the speed of the ship in the direction of the run of the waves. The constancy of these speeds in time;

Constancy of the setting, the angle of heeling, of the

trim and of the drift in time, guaranteeing thé constancy of the heeling momentum in time;

Theabsence of lateral hydrodynaniic forces.

rethod of the Experiment

It would appear that the most effective experiment could be carried out with a self-propelled model with an automatic

rudder, an automatic speed regulator on a regular wave, However it seems that the difficulty of rigging such a model has also other technical difficulties.

The model should have aspeed acceleration zone, with constant speed of waves. In this sector the application of the heeling momentum will produce rolling of the model. As a

distance after achieving the given speed before constant heeling, angle of drift, setting and trim are determined and it becomes possible to carry out the essential measurements. The presence of lateral speed of drift will inevitably push the model to the edge of the basin. The width of the basin therefore, should be

sufficient that during observation in the sector of even

movement the effect of the walls does not influence the results. The automatization of directing and measuring will recuire

considerably larger models and therefore also a larger basin. High requirements must also be assigned to the wave maker,

since irregular waves or their subsiding at increased distances from the source will change the conditions of the experiment,

Fluch simpler would be the setting up of an experiment with a non selfpropelled model in a basin of dynarnornetric type.

The suspension of the model to the carriage should ensure free floating, trimming, and heeling of the model and its free

shifting across the carriage (freedom to drift). In this

event the sector of acceleration may be reduced, but all the other considerations listed above retain their validity.

In gravitational type basins, adequate testing is practically impossible since even harnessing of the model excludes freedom of drifting; the small length of the basin does not permit enough time to attain movement nor to carry out - the subsequent nieasurings; the movement of the model in

relation to the observer does not permit the necessary visual observation.

A decided simplification of the experiment may be achieved in a hydro trough. The hydro trough permits full reversal of

movement where the ship and the profile of the waves is static in relation to the observer, but the current flows against the ship at a given speed. The time of regulating the model is not limited by the possibilities of observation; the measuring of

shift, of the forces, and of the momentum are not limited as to time and are considerably simpler than in a basin.

The relatively narrow width of existing hydro troughs does not permit the achievement of free drift of the model. However,

there is a possibility of a somewhat different manner of setting up the experiment. Inasmuch as actual observations do not uncover significant drift with heeling and rolling while moving, it is

logical to assume that the rate of drift, and therefore the angles of drift are small. Therefore, for the determination 01' "pure" recuperative momentum in the hydro trough it is possible to

assign to the model such a fixed angle of. drift under which the lateral force of drift becomes equal to zero. The

suspension of the model for this, permitting free heeling, floating and trimming, should be reversed in relation to the vertical axis. The possibility must also exist to measure the

force in any given position of the model.

and the speed of drift

VgtJp sin 10

(iLk)

where is the speed of current in front of the ship In eouìtion (9) the third member will be absent with this, as in the situation of the stooping of the model

R70

upi

tnd the recuperative momentum on the move is determined as per usual conditions:

M= Meq)

For an experiment on a wave the latter may be createJ on the surface of the current by means of submerged crosswise baffle plates on the bottom of the trough in front of the

model. As preliminary tests in the trough of the Institute have shown, the height of the waves can be contr1led by

changing the form and hei'ht of the baffle plate, the phase of the waves at the stopping place of the vessel can be

With such a setting up of the experiment for movement

on cairn water complete resemblance to nature will be achieved .inasrucb as the equations of equilibrium are quite identical. It only needs

to be considered that for the speed of the ship in this, a projection of the vector of the speed of the current on the diametral has to be assumed, that is, (Figure ₃₎

ZJ,= V CUS 13o,

changed by shifting the baffle plate along the axis of' the current, and their length is related to the relative speed of the current (3). The halting of the model in a balanced

position on the wave is analagous to its position in _{a current} of "calm"water.

It has to be pointed out that such an experiment in _the hydre trough differs in one respect from a test with _{a model}

in a basin when the model has L1 stages of freedom. In the basin the vector of the resulting speed is inclined _{at the} angle _{J3., to the direction of' the course of the waves, but} diametrically perpendicular to the crest of' the wave.

(Figuré 2). _{In the trough the vector of the resulting speed}

is perpendicular to the crest of the wave; but, the diametral established the angle (Figure ₃₎ with the direction of' the course of the waves.

The experiment in the trough thus corresponds to the

event when the course of the vessel does not lie exactly along

the accompanying wave, but at some taper . Inasmuch as

the angle can be expected to be quite insignificant, particularly with small and medium angles of heeling, this difference, it seems, may be disregarded.

LI TERATIJRE

S.N. Blagoveshchenskiy. "Submission concerning the

standardization of the stability of large and medium commercial fishing trawlers." LK1 (report on blueprint).

S.N. Blagoveshchenskiy. "Submission concerning the standardization of' fishing seiners." LKI. 1958 (Report on blueprint).

3 "Transverse stability of tunny clippers." Material from the presentation at the II World Congress on cournercial fishing vessels. (Rome 1959).

Issue 3L4

Fishing Fleet Publishers,

_1960.

Lj Collection of material of the International Shipbuilding

Conference. Shipbuilding Publishers,

_1957.

Grim. "Rolling Stability and Safety in Sailing." Ship technics, 1952, issue 1.

Upahi, E. "Reflections on Stabilizing Procedures in Sailing." Shipbuilding technics, issue 9, Sept./Oct. 1961.

Wendel, K. "Loss of Stability in Sailing and Through Coke Deck Cargo." Hansa,

1954, p.

_2009.

CONCERNING THE INPL5ENCE OP SPEED ON THE STABILITY 0F' A VESSEL

by Yu. I. Nechayev.

1. STATEMENT OP PROBLEM

With movement there occurs a redistribution of pressure in the submerged part of the hull as a result of which the

re-cuperative momentum changes.

Papers are available (i), (2), in which changes in stability while moving are determined experimentally _{as well as} theoretically. However, the study of this problem in the quoted papers applied only to the determination of the influence of speed On initial stability.

Table 1.

Characteristic of models Modelled

SRT ships MRT 60 Series Scale 1:140 _{1:25 1:125} L, cm

_86,75

_82,3

_97,6 L B _14,82

_3,21

_7,50

B T _2,148

3,11

_2,140 H T _1,20 1,146 1,514

s

u

0,58

0,83

0,14145

0,72

0,60

0,75 0,814

_0,73

_0,98

Initial Netacentric height _0,0673 0,11B _0,05B

Applicate of centre of value

_4,38

5,02

3,00

Relative applicate of fastening point of model

0)

AWVA

Ii

W1ri'

'Nittqi

_{Iii Willi}

58.11 h 5.fl 38.17 28.11

f 5.17

'igure L Theoretical Diagrams of hulls of

models of researched ships.

iiL1 2021

TEA FA

ariwn

71111

II

I.

II

Iv ¡JI ¡T

f

1711 1

¡t I, z.

II 5 5J7 48.,? 38v? 2 D.s? f 5? 68.fl 58.i? 'i 8.17 3 8.,? 2 8.,7 f

a. SRT with quarter deck; b. NRT of KFK type; y. transport vessel of the 60 series.

The aim of this research was the experimental determination of' the influence of the Froude figure on the stability of a

ship. For this, in contrast with other studies:

The stability diagram was taken dowii fully to the angle

of roll.

The value of the lateral hydrodynamic forces acting on a moving and heeling model was determined and the influence of the

error on the results of the experiment was evaluated.

The models of three vessels were selected as the objects of research:

a medium fishing trawler type SRT with a oüarterdeck; a small fishing trawler type KFK;

a transport vessel of the "60 series".

The theoretical body diagrams are presented in Figure 1;

the main measurements and characteristics of the models in Table 1.

2. DESCRIPTION OF EPERINENTAI EQUIPMENT AND THE EVALUATION 0F THE INFLUENCE OF THE WALLS OF THE HYDRO TROUGH ON THE RESULTS OP THE EXPERIMENTS.

The testing of the models was carried out in a hydro trough which had the following characteristics:

Working cross section - width 1 meter, depth o.8 meters. Maximum speed of current - around 2n1/sec. The range of speeds with the method of actuating the fluid, used in the experiments, was practically uniform. During the time of the

tests (Figure 2) the model was held in a special suspension 1,

which permitted free heeling, trimming arid floating of the

model.

_{The suspension, together with the carriage 2, moved}

along the working part of the hydro trough.

Figure 2.

Model with attachments during the test period in the

working part of the hydra trough.

Heeling of the vessel was achieved by shifting weights

on the heeling directing device 3.

The angles of heeling were

determined by a bank indicator L

In order to obtain the experimental points on the

falling branches of the stability diagrams, apparatus 5 was

used, by means of which the position of the unstable balance

of the model at a

iveri heeling momentum was determined.

Positioning of the model without heeling and trim on calm water

was done by means of a levelling indicator attached to the

model.

In order to evaluate the influence of the walls of the

hydra trough on the results of the experiments, tests with a

comparatively wide model = MRT (the lengths of all models

was approximately equal) were carried out.

The tests confined

themselves to the deteriuination of the changes in

the

recuperative momentum in relation to the distance

of the walls

from the model which was varied by shifting

duplicate walls

across the working uart of' the hydro

trough.

The results of the tests are shown in Pigure 3; along the

axis of' abscissa of the

quantityb

--

,

where b- is the width

of the working part of the hydro trough, y is the distance

of

the wall from the closest part of the lateral surface

of the

model in straight position; along the ordinate axis is the

value

whereA4

t

are the stability arms

of the form with and without movement.

The qjoted values AC

corresponds to the positioning

of the swivel at the centre of gravity of the model.

3

Fire 3.

Curves showing the relationship of the value

of

the distance from the walls for model FIRT.

0004 0002 ¿ 006 00!?4 ¿ 002 0.008 0005 o004 0,002 -2 I

j

0. 5

il

J

T

-fr -023 I -fr 0,28 I

-ß

Pr '03f .2 , 3 4

r

The tests were carried out withthree Froude figures: Fr = 0.23; Fr = 0.28; Fr = 0.31; embracing the range of speeds of the researched types of vessels.

As can be seen from Figure

_3,

_{influence of the basic} walls on the recuperative momentum at the _{range of movement}

used in the experiments is absent.

). PROCESSING OF RESULTS OF EXPERIMENTS

In papers

₍₃₎

_{and () it was shown that the recuperative} momentum observed in tests with non self-propelled models

includes a supplementary hydrodyriamic momentum from the lateral force of drift. _{The lateral force develops as a result of}

the destruction of the symmetry of flow by the submerged part of the hull when the model travels with heeling.

Let us study the condition of balance of the model fastened at point P and moving with speed _{y (Figure Li).}

Figure Li. _{Sketch of the forces acting on a model during test} -period.

Joint P permits the model to heel, _{trim and float freely} but does not permit sideways movement.

When the model moves with heeling, lateral hydrodynarnic

force develops and a horizontal reaction occurs in the

joint P.

In this event the niomenturn equation looks as follows:

Dl9 - ¡

[(z,, - z1) cos O + y, sin O] =

(i)

where D = water displacement of model;

'ev =YCJ COS U + Z1 sin U - Zg sin U;

R7 = lateral hydrodynamic force;

Mkp_ the given heeling momentum;

z

= fitting of fastening point of model;

fitting of force R

= angle of heeling.

The equation

R I(Zp z1) COS 0 + Yc sill f)]

represents the supplementary momentum, developing as a result of

the limitation of drift by the model.

Let us study the influence of force R7 on the magnitude

of the recuperative momentum.

Let us imagine a vessel, heeling

at an angle of e at the start of drift, that is, when lateral

speed is equal to zero. In that situation, lateral hydrodynarnic

force R7 will also act on it

as well as the corresponding force

of inertia, which is equal to it and rests in the centre of

.gravity of the system.

Force R7 diminishes in proportion to the

increase in the speed of drift and at a steady speed it will

be equal to zero.

Therefore the recuperative momentum at the start of

Dl9

- R

[(Zg z1) cos O + y1sinO}.

Actually the vessel will heel in the observed angle O during some time and force R1 will increase constantly. Consequently when heeling of the vessel reaches the angle e the vessel will

already have some speed of drift, and the lateral hydrodynamic force will be less than value R7

If it is taken into consideration that the point of application of the force of inertia, taking into account the adjacent mass of water, in actually is below the centre of gravity of the vessel, then it is obvious that equation (i') represents the lower limit of the recuperative momentum which

in nature can only be achieved with instantaneóus heeling of

the vessel. We designate this momentum as the minimal recuperative momentum at a given heeling angle O

M9

min Dl9 - R

í(z - z1)

cos O + y, sin OJ,

where Zg = application of the centre of gravity of the model. In this way, in order to obtain value Mev,9. it is

necessary to locate hinge P (see Figure Lij) at the centre of gravity of the model.

The value of the recuperative momentum at smooth drifting may be obtained by placing the model with the angle of' drift

in the direction of the speed of flow in such a way that force is equal to zero. However, it has been established

through tests that, with slight submerging, it is possible to establish the value of the recuperative momentum at the

line of action of force R with the condition that it passes through point CO3 that is the centre of the volume of the model in a static position. For this reason in order to obtain the

value of it is necessary to place hinge F at point C0.

The two values of the recuperative momentum established in this manner characterize its extremes at a given angle of

heeling.

Because it is not permissible to shift hinge P in the

centre of gravity and in point C (this inclines to restrict the angles of heeling) during the experiments, the minimum and

maximum recuperative rrjomentum is determined by the following calculation:

M0_omm

=M

+R,1(ZpZg)COSO, M9

= M + R,1 (z,, - z0)

cos O.

vmax

The arms of stability of the foriii in this instance will be:

I R vmn D

+--(z,, Zg)COSO*asIflO,

where a=Z - Z g CO MKP R,1

max =

+ -_ (z,, - z0)

cosO +asin O,

The value of the lateral R1 may be determined by direct measurement on hydrodynamic scales as well as by formula (6),

see below. For this it is necessary to set up two momentum equations, one of which refers to the position of the hinge at point P, and the other to point P1 (see Figure LiP). The

heeling momenta with this should be selected in such a way that the heeling angles in both instances are the same. Then

(3)

force RV is found fron the following equation:

R MKPMKp_zcosO

where M and is the heeling momentum with hinge positions

at noirits P and

Êz=zp1

_{- zp.}

The conclusions obtained apply fully to the event of the movement of the model on an accompanying wave.

4. TLT$ O' TIIi LX2iRIiENTS

The diagrams of the relative arms of staility, based on these tests, are presented in Figure

_5.

The agnitude of the lateral hydrodynamic force was established through equation (6).

The curves ffor the selected Froude figures are

shown in Figure &.

As cari be seen from the drawing, the magnitude of force essentially depends on the Froude figure and the angle of heeling. Jith a 40° heeling angle, and a Froude figure O.l, force attained the following values in the tests:

2% of water displacement of MRT;

l.5

of water displacement of SRT;

0.8 of water displacement of vessels of "60 series;

The quoted values in nature represent:

R7 = '4'.6+t for MRT at D = 232t.

R7 ₌ 6.5?t for SRT at D = 438t.

R7 - for vessels of "60 series" at D 8050t.

0.03 0,02 0,0f

IQ

20.30

40 50 60 6,2ptuY

Figure 5.

curvesf(e,h)obtainea

in experiments: a model SRT;

b model MRT; y model "60 series"; i - Fr 0; 2 - Fr 0.23;

3 - Fr - 0.28; Lf _{- Pr - 0.31,}

20 30 40 50

a) Q025 0.020 0;0f5 0; 0'O 0,005 fO 20 JO 40 50 epa'ö 8) e) o;ow 0,025 0,05V 015 4OfO 4005 20 30 40 50 epa!

F4.gure 6. Curve

i%irf(r)

_{; a - model SRT; b - model MRT;}

y - model "60 series"; i - Fr _{0.23; 2 - Fr = 0.28; 3 - Fr = 0.31.} A Froude figure 0.31 turns out to be too high for these

types of vessels, therefore value _{in nature is determined} with a Frde figure of 0.28 which corresponds to actual conditions when these vessels move at the following speeds: - SRT - 10 knots.

19RT - 7.8 knots.

Vessels of the "60 series" _{- 18.9 1ots.}

The value of R with a Froude figure of 0.28 in tests with

1.25 % of water displacement of SRT; = 5.48t;

0.65 % of water displacement of vessels of "60 series";

_52.3

t.

Although the magnitude of the lateral hydrodynarnic force is relatively small, disregard of it will have the consequence that it will be possible to obtain different stability diagrams in

relation-ship to the point of attachment of the model (Figure 7)

0.020 018 0.016 0 0f4 C12 0 OfO 0,008 0.006 O 004 4002

uusuuuiu...a

UU/4 Pr0

...wi

_'6

_uUiUii.

...'i 7 'I4 w'i. -, , riiu..

u.uii.itu.

auu.uuuuuuusu&ivar.&

Figure 7. Curves showing the relationship of the curves of

stability of the SRT model to the point of attachment of the model. Also studied during the experiments was the effect of speed on the metracentric height. The results are illustrated in

Figure 8 by means of curves.

.0z

'

or O2 ¿25 0,30 t33 Pnc. 8. KpHfmle = f(Fr) Figure 8. Curves -

5(fl)

ah B 50 60 9,epañ 'O 20 30 40

where 4h = h1h;

h0 and h are initial lateral rnetacentric height in presence and absence of inovement respectively.

Tests have shown that initial stability in these types of vessels increases with a growth of the Proude figure. The

h presented in Table

values are 2.

In Figure 9 curves illustrating the changes of the relative arms of stability of forrnLvmÑ. B in relationship to the angle of heeling and the Froude figure are shown.

e) 10 20 30 40 50 'V 0,006 çO3 û vow fr'02S 10 20 30 40 50

Figure

9.

Curves=J(&rith hinge P attached in the centre of gravity of the model.

Table

2.

Vessel

Value --- obtained Value in nature,

ein in tests Fr0 2:3 ?r=0 ,28 FrO , 31

Fr0 23 Fr0 28 r=0,31

S RT MRT Vessel "60 series" 0,002 0,006 0,001 O ,OOLI.5 0,0120 O 0017

Q 0057

0 0180 O 0023 1 ,+4 3 ,8L 1,62 3,2Ll 7,70 2,82 4,1O 11,50 3,7L 8 78 ¿004 fr°23

The valueAC was determined as shown in paragraph 2. In

order not to clog up the graphs the valuee.B is not included

in Figure 9

From Figure 9 can be seen that with large heeling angles at increased speeds the arms of stability grow for models T4RT and for the "60 series", but diminish for SRT.

The maximum and minimum increases of the relative arms of stability of the form for a heeling angle of Li0° are shown in

Table

_3.

The upper figure in each graph of this table corresponds to the minimum value of , - the lower to the maximum value.

It is interesting to note that the I'1RT has sharper outlines

than the SliT. However, the stability of the NRT at large angles of heeling increases with a growth of the Froude figure, but for the SRT it decreases. This does not contradict the conclusions reached in treatise (2) and can be explained by the fact that

these vessels have a different relationship of the main dimensions, particularly L . As a result of this the character of' wave

B

making, with which basically the changes in stability with

movement are deten.nined, are different for NRT and SRT with the Froude figure used in the experiments.

Table

_3.

Model

Valueobtained

Value in nature, cm

in experiments

Fr=fl,23 Fr=O,28 FrO,3I Fr=O,23 Fr=O,28 Fr=O,31

S RT 14 RT Vessel "60 series" -0,0023 -0,004 -0,0055 -1,67 -2,88 -3,90 -0,0005 -0,002 -0,0030 -0,36 -1,45 -2,16 0,0038 0,0054 0,0077 2,44 3,46 4,$3 0,0060 0,0090 0,0106 3,84 5,75 6,80 0,0016 0,0032 0,0046 2,60 6,17 7,47 0,0022 0,0039 0,0054 3,58 6,33 8,75

The research carried out to determine the influence of the Froude figure on the stability of ships' travelling on cain) waters permits the drawing of the following conclusions:

The stability of a ship changes with movement and the change

incrcajeS with an

increase in speed.

The changes in stability are particularly noticeable with relatively high Proude figures (from 0.25 and up), which cari be explained b; extensive wave development at

given

levels of

movement.

The character of the changes in stability depend on the

relationship of the rain dimensions and shìpe of the hull. The

changes in

stability are different for different vessels which were studied:

1. Initial stability increases with an increase in the Froude

figuro.

3tability nd high angles of heeling increase with an increased Froude figure for vessels of the NRT and "60 series" type, and

deôreases with the RT.

e.) Lateral

hydrodynarnic

force exerts a considerable influence on the stability of a vessel. The magnitude of this force grows with an increase in the speed of movement and the angle of heeling, its influence becomes apparent considerably after the entry 01' the deck into the water because the flowing around the hull changes sharply.

d) 3peed of movement influences stability in practically all coInliercini vessels, since, despite the slow speed of these

vessels, their Froude figure is relatively high.

The determination of the changes in stability during

movement by theoretical methods is specially difficult. This can be explained by the fact that with tilting of' the vessel the

character of wave formation along the deck alters and to determine the surface on which the pressure field has to be integrated is practically impossible. It is possible to solve this problem for low Froude figures when it is possible to

disregard wave formations, but this is of no interest since the changes in stability in this case are insignificantly small. In this connection there are two ways by which changes in stabiliy while moving can be determined:

Testing with the model of the ship which is to be researched; An approximation by means of graphs and diagrams constructed

on the basis of systematic model tests.

LI TERATTJRE

Baker, G.S. The effect of longitudinal motion of a ship on its statical transverse stability. Transactions of the Institute of Naval Architects y. 60, p. 71+_80, 1918.

2. Bazilevskiy, A.N. Concerning the effect of speed on its

transverse stability and deck rolling. "Naal Fleet" No. 1.

_1956.

Sevast'yanov, N.B. Stability of a vessel travelling on calm water and an accompanying wave. Proceedings of the Kaliningrad

Technical Institute of the Fishing Industry and Nanagement, issue XIV.

_1962.

1+. Nechayev, Yu. I. Experimental study of the stability of models

on accompanying waves. Lecture at the XIII Scientific Technical Conference on Ship Theory (Krylov Lecture). 1963.

by Yu. I. Nechayev 1. STATEMENT OF PROBLEM

Several papers devoted to the stability of ships on an

accompanying wave, permit taking into account the effect of trim on the stability of ships when statically placed on a wave (l-9). But

experimental research carried out in the Department of ship theory of the Kalinirigrad Technical Institute for fishing industry and management (10) shows that the stability calculations with a static

position on a wave may lead to considerable errors for ships of small length. The main reason for this is interference of free and ship's waves, as a result of which the profile of the free waves changes and changes into a wave of Irregular form. To

Illustrate the influence of interference, stability diagrams of Seiner SO, the medium fishing trawler type SRT with quarterdeck and transport vessel of the "60" series are presented in Figure 1.

The SRT model had a superstructure and a deckhouse in-cluded in standard stability calculations; the model of the seiner SO and the transport vessel of the "60" series were tested with a smooth deck. The characteristics of the vessels are presented n

Table 1.

The experiments were carried out in a hydro trough on

waves. _{The length of the wave was equal to the length of the}

ship. The relationship of the height and length of the wave

The stability diagrams in Figure 1 conform to the fastening being in the centre of gravity of the model. From the drawing it can be seen that, with an increased

relationship L, the influence of interference diminishes B

and the experimental data approach the calculated data. It has to be pointed out that even with consideration of the hydrodynamic pressure in the wave (consideration of the Smith effect.) for ships of short lengths, the size of difference of the experimental data and the calculated ones remains quite considerable.

Table 1. J B B T H T initial rnetracentric h e i gh t Proude Figure of tests Characteristics of Models

4 ,3

2,92 1 , 41 0, 1025B

0,316

Modelled Vessels Ll,82 2 , 42 1,18 o ,118B O ,28

7,50

2,40 1 514' O ,05B 0,21

As a result of this the changes in stability in relation to the trim in this study were determined experimentally. Ships of two types of commercial vessels were tested: of the medium

Scale 1:25 J, :40 1:125

L, cm 100

_86,75

97,5

and small fishing trawler, and furthermore the model of the SRT was tested in three variants: smooth deck, with a fore-castle, and with a poop.

The measurements of the forecastle and the poop are: length - 0.2 the length of the ship, height - standard height of superstructures.

The selected types of ships differ in a considerable degree in the shape of the stern (SRT has a cruiser type, IIRT - a transom type,) and consequently, also in the relationships of the main measurements (see Table 2).

a) 4aJ £8Z F) e. 7 005 40J 402 a

A.

/6 /5 96 z 7, I. 29 Jo 68

Figure 1, Diagrams of static stability of SO, SRT and vessels of the "60"series;

aSO; L = 4.0:3; bSRT; L='+,82; y - vessels of the '6o" series;

B B

L=7.5; 1 - on calm water; 2 - on the crest of the wave (exper-imental data); J - on the crest of the wave (calculated data).

All the models were tested with a Froude figure of 0.28. The length of wave for SilT was 78 cm. and for NRT - 98 cm; height

Jo

20

height h

- 5.2 cm. The profile of the wave was close to sinosoidal. The basic assumptions accepted when transferring the results of the experiments to nature were the following:

The speed of the ship is close to the speed of the run of the waves, as a result of which the period of sojourn of the ship in the determined position on the wave was sufficient so

that the ship would incline to the critical angle under the effect of the given heeling momentum;

The vessel can be steered; the turning momentum created by the hee1in can be compensated for by turning the rudder; the maintenance of the longitudinal axis of the ship (the course)

can be safeguarded perpendicular to the crest of the waves.

Table 2. Characteristics of model SRT clear deck SRT with forecastle and poop MRT Scale l:-i'O l:L0 1:25 L, orn 86,75 86,75 82,3 L L,82 LF,82 3,21 B B 2,81 2,7LF 3,20 T II _1,37 1,33 i

,La5

T 0,55 0,55 O , LL ct 0,80 0,80 0,71 0,81 0,81 0,72

The tests were carried out in a hydro trough.

The lateral hydrodynamic force produced by the heeling

during the movenent of the ship in this event was no-t

determined by an equation but by hydrodynarnic

scales (Figure 2).

Figure 2.

3ketch of Flydrodynarnic. 3cales.

Iiydrod.ynamic scales are based on the principle of

guiding the acting forces towards zero and consist of -two

parts:

The actual scales levelling of the lateral force in

relatioii to the axis 0

-

0h,, and

$usnension scales insuring the models freedoi

of

heeling (axis °l

_-

,

trim (axis 02

-

2) and floating

(axis 03 - 03).

hnitb weights P1, P2 and P3 the suspension balances

in relation to axis 01 -01, 02 -02, and 03 - 03.

Weights

P1+, 15 and i]6 are designated to

balance all the loads in

relationship to the axis Oj+ - 01+.

on the arm 1. Then force R7 is determined from the relationship:

P ₁ - R _l2

Arm 12 is the distance between the parallel axis

01 01, and

- It changes with the changes in the rate

of movement and the angle of heeling. As can be seen from the

drawing, 12 consists of the constant value AB and the variable CB1, which can be determined by the indications of an arrow fastened at point B1.

In order to create waves in the hydro trough, a wave maker rnáde in the shape of a stream lined baffle plate was

used. By means of changing the length and height of the wave maker, it is possible to obtain, with a predetermined speed, waves of varying parameters.

3.

PROCESSING OF TEST )ATA

The processing of the data from the tests (Figure ₃₎ was carried out, taken into consideration the influence of lateral hrdrodynainic forces, as follows:

1. The stability diagram on the wave at the height of the point of fastening used in the test was determined;

2, The value of the lateral hydrodynamic force was determined;

3.

On the basis of the conclusions reached in the article "concerning the influence of speed on the stability of a ship" (see article on p. 160 of this issue), the test data were

0.011

8/12

0,Of

41k

iL

11

10 20 30 40 J0 60

Figure

_3.

Stability diagrams of SRT.

1, on calm water; 2 on the crest of the wave (fastening point in the est) ; 3 on the crest of the wave (point of fastening

irt centre of gravity of the model); k. on the crest of the wave (taking into account the angle of drift).

As a result of this, the stability diagrams at multiple heelinge of the ship, when it had not yet achieved the speed of drifting, were determined. The arEis of stability in this event at the given angle of heeling are minimal.

Under the action of the lateral force, the ship starts to drift and with a steady drift, when the lateral force R1 O, the ship will move with a certain angle 92 of drift (li).

Stability diagrams with a steady drift were determined in the test in the following manner.

At a given heeling momentumM' , force R1 and anglel-were determined on the hydrodynainic scales, after which there

forms drift angle Ç' so that the lateral force was equal to zero, With the determined angle

1 and momentum1V1i the angle of

the stability of the forn in this case practically does not differ

frani arm

In the presented diagrams (Pigures

4,5,

and

₆₎

with the aim of summarizing the total number of graphs, only the minimum

arms of stabilitye Mare given.

In order to obtain the

va1ueOri

it is necessary to add to the value

-to

on

the diagrams the correction1ê

, then

=

_min+ 1lo.

y max

The va1uel

for the researched ships is given in

Table ₃

In the numerator - on the crest of the wave. In the denominator - in the trough of the wave. The values of the corrections in dependence on the drift are not quoted because the changes of the lateral

hydrodynarnic forces resulting from drift give a correction

considerably less tbanlQ

Vessel Modelled ValuelO in Nature Table

3.

corr O 20k' O = 300 O 40° CPT MPT o

_0,79

1,7 0,1 0,62 0,5 6 1,15 1,1 0,25 0,61

consisted of the following:

An angle of trim which was measured in a level position of the model on calm water was assigned to the model. _{At the} given angle of trim the stability diagrams were determined; a) _{on cairn water, b) on the crest of the wave, and y) in} the trough of the wave.

Ce B o,û «05 ¿1,04 4 0,0

4

5 /0 20 Jo ¿0 50 10 79

Figure 4. Stability diagram of a clear deck model of SRT.

1,2,3, - on the crest of the wave; 4,5,6, _{- in the trough of the} wave; 7,8,9, - on calm water; the trim on the bow corresponds to curves 1,4, 7 on the stern, 2,5,8, _{on an even keel - 3,6,9,}

The construction of the diagram consisted of the

determination of the angle of trim at a given heeling _momentum. The centre of gravity of the model with changing angle of -trim remained constant.

All the models were tested with an angle of trim _{= 2,5e,} while the model with a poop was tested with _{a trim at the}

stern, the model with the forecastle only with a trim at the

bow. The angle4J =

_2,5°

_{corresponds to a trim in nature ofT}

wave before setting at even

keel were determined.

The results of the tests are presented in

Figures L,5, and

6.

since the changes in the arm of

stability in the NRT model

are relatively not very large, there is no necessity of

coordinating the diagram on one chart as was

done for the SRT.

a) 4

q

/0 20 30 40 £0 50

Figure 5.

Stability Diagrams.

a - 3RT model with

forecastle; 'o - SRT model with poop; 1. on

the crest o± the wave with trim; 2. -

the saine without trim;

3. - on calm water with trim;

.

- the same

without trim;

5. - in the trough

of the wave with trim; 6. - the same without

trim.

From Figures 1+,5, and

6 can be seen that the influence

of trim at the crest or in the

trough nf waves is different.

The trim on the bow of models of SRT

(Figure Lf)

and

NRT (Figure 6) when located at

the crest of the wave in

comparison with setting on an

even keel

increàses the arm

2f 05

L

Jo 40 58 ñ7 B ¿O5 £05 004 003

of stability somewhat on the rising curves of the stability diagrams and lowers them on the failing ones by about the same degree of intensity.

'1hen placed in the trough of waves the trim

on

the bow

(Figures 1.,5,

and 6)

leads to a sharp drop of the arm of

stabilit; at ail angles of hc°ling. A particularly decisive lowering of the arm of stability occurs

in

the hPT models tPo stabiljty,Jiararns of which under trim at the bow, in the

trough of the wave, is lower than that of tile stability diagrams

on calni water (curve ₃ in Figure 6h). The lowering of stability in the trough of the wave under bow trim

can

be

explained by the increased flooding of the odel from the bow, since, starting with a certain angle of heelinL, the bow of the model submerges into tPo crest of the waves and tile flowing around the hull changes sharply. It has to be noticed that with MRT models with relatively small saddlini, even in the

position in the trough of tile waves without trim (curve

3 in

Figuro 6a) the increase in the arm of stability is very small.

With trim on the bow the influence of the forecastle which was set up on the model SRT was observed. Tests showed that

when

located on the crest of the wave (Figure a, curves i & 2)

the influence of triiri remains the

same as

with clear

deck

iuodels (Figures curves i &: 2). When located in the trough of the wave the presence of the forecastle markedly reduces

flooding of

the model from the bow, and with trim on the bow

of ' i.5°, the rising curve of the stability diagrams (curve on Figure 5a) rises for a considerable distance somewhat higher than in the diagram with o. This can

be explained by this that with the submerging of the bow end the frame of the forecastle enters into the water, having considerable flow it creates a supplementary backwater of the current in

the area of the bow.

The trim on the stern when. the model SRT is placed on the crest of the wave (Pigure L1, curve 2) led to a reduction of the arm of stability at all angles of heeling in comparison with position &p = 0. In the model MRT the arm of stability

changed only insignificantly with this. When placed in t!ie

trough of the wave the trim caused considerably fewer changes on the arm of stability on both models SRT and NRT than

at t.,)' .0.

The influence of the poop was determined-with trim on the stern. The tests showed that with the presence of a poop the trim at the stern at/) =2.5° increases the arm of stability on the crest as well as in the trough of the wave (Pigures 5,6).

The increasing values of the arais of stability are presented in Table L for comparison.

The increasing values of the arms of stabuity(q)c14which are created by the trim of the models at ' =

2,5°

and angles of

heeling of 20; L0° are presented for comparison.

Thevalue?,)&?was

determined as the difference.

-

(') lv'

- is the arm of stability of the shape of the model with trim on waves

- is the arm of stability of the shape of the model at the same angle of heeling, but without trim.

a)

-3

«o4 «03 «02 «o' «04 «oj (702 «01 «04 (783 4782 4'Ol (0 28 38 40 58 ¼

Figure

6.

Stability Diagrams of MRT Models.

a - without trim; b - with trim on bow; y - with trim on stern;

1. on calm water; 2. on the crest of waves;

_3.

on the trough of the wave.

From Table L can be seen that changes of the arm of

stability of the shape of the models with trim on the crest of the wave are not great and influence stability diagrams only slightly, while with t'irn on the bow in the trough of the wave the arm of stability diminishes sharply.

CONCLUSION

0n the basis of the work carried out in studying the influence _of' trim on stability with accompanying waves, the following deductions can be drawn:

1. When the SRT and MRT are placed on the crest of the wave,

at large angles of heeling, wi-th trim on the bow as well as the stern, the arms of stability actually diminish.

Table 14.

INCRJASE OF TItE AiJ OF STABILITY 0F TIDi 1?ORI WITh TRIM

Value()j4 in nature, cm

3ituation stud i ed Vodel on crest of wave Nodel :Ln trough of wave S clear deck SilT with forecastle SilT NPT with poop

In the numerator with trim on the bow; in denominator, trim on stern.

2. _{Vihen the ships under study are placed in the troughs of the} waves, trim on the bow leads to a sharp reduction of the arm of stability at all angles of heeling in comparison with an even keel position. While with an NRT at not very high saddling and a low, above water deck, trim on the bow will cause the bow of the vessel to dig into -the crests of the waves, as a consequence of which flooding worsens and the stability diagrams in the trough of waves rray be located even below the stability diagrams on calm water.

. Trim on the stern in -the trough of the wave does not

affect stability significantly.

. The presence of a forecastle increases stability in the

trough of the wave, with trim on the bow, in comparison to _n

200 3oj 400 120° 300 _400j 200 _{30° - -i 20° 30°} I 4Q0 1,08 -1,4 -1,8 -1,3 0,5 2,2 0 -0,7 0 -0.5 -2,1 -1,1 1,8 2,2 3, t

-0,5 -1 -1,9

-4,4 -5,8 -10 2,1 2 1,4 -4,5---4,2 -3,8 -2,11-2,2 -1,8 2,9 2,1 2,2

-0,4Th2

even keel position and affects the position on the crest of the wave only slightly.

The presence of a poop increases stability with trim on the stern (on the crest as well as in the trough of the wave) in comparison with an even keel position.

The value of the reduction of stability on the crests of waves with superstructures (forecastle or poop) continues to be quite considerable.

In this way the research showed that frein the point of view of insuring stability, trim on the bow of a ship when travelling on accompanying waves should not be permitted, since its stability may be much worse not only on the crest of the wave but in certain circumstances in the trough of the wave, than when travelling on calm water.

LITERATURE

1. Basin, A.M. Deck rolling and stability of ships on waves. Proceedings of TsNIII4F (Central Scientific Research Institute

of the Sea Fleet), series "Sea transport", issue XXX, 1955.

2,

Blagoveshchenskiy, S.N. The stability of vessels on the crests of waves. Lecture at the IX ScientificTechnical Conference on ship theory (Krylov lectures), 1958.

3.

Boroday, I.K. Transverse stability while moving on waves. Proceedings of the IsNil (Central Scientific Research Institute), named after academician A.N. Krylov, issue 191, Shipbuilding Publishers,

_1962.

+. Voyevodin, N.F. Statistical stability calculations for ships on accompanying waves - Shipbuilding, No.

7, 1963.

Nal'tsev, N. Ye.., Kogan, A. Sh. The construction of

statistical stability diagrams for vessels sailing on lateral

waves. Shipbuilding, No.

7, 1963.

Arndt, B., Roden, S. Stability with encountering and

accompanying wave. Journal "Schiffs technik" Vol. 9, No. Lf8,

1962.

Arndt, B. Sonne stability calculations on waves. Journal

"Schiffs technik" Vol.

9, No. k8, 1962.

Paulling, I.R. Transverse stability of tunny clippers. Pisbing boats of the world, 2 London,

1960.

Paulling, I.R. Transverse stability on longitudinal waves. Journal of Ship Research, Vol.

k, 1961.

Nechayev, Yu. I. Bxperimental study of the stability of models on accompanying waves. Lecture at the XIII Scientific

Technical Conference on Ship Theory (Krylov lecture) , 1963.

Sevast'yanov, N.B. Stability of a ship when travelling on calm water and on accompanying waves. Proceedings of Kaliningrad Technical Institute of Fishing Industry and Management, issue XIV,

1962.