Stability of beam-trawlers in following seas

1)

LABORATORIUM VOOR

SCHEEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFT

r

january

1971.

Stability of beamtrawlers in following seas by W. Beukelman and A. Versluis

T

Report No.

₂₉₅

141

Sunixnary

The transverse stability ha experimentally been determined for the models of four beam trawlers with various prismatic coefficients and constant block coefficient, travelling both in still water and in a following wave, In still water three speeds have been considered and in a following wave with wave length equal to ship length one speed, slightly less than the wave celerity has been considered. All models have been investigated without bulwark ,with closed and open bulwark.. In addition static stability calculations havebeen made for still water and for the case of a model on a wave crest, both for speed zero1 The results of the computations and experiments are compared with each other. The experimental and calculated reduction of the righting arm agree very well for the model with the

highest prismatic coefficient, while for the other models the experimental reduction is less than the calculated one.

From the experiments the speed influence on the righting _{arm in still water}

followed; in generala gain in tabilîty was found. Further the experimentally determined curves of righting arms of the different models are compared mutually and additionally the calculated curves too.

Finally the righting arm in relation to the prismatic coefficient is represented for still water, with and without speed and for the ship in the crest of a

1. Introduction

At the request of the Technical Research Department of the Fisheries

Directorate of the Dutch Government calculatIons and experiments concerning the transverse stability in following waves have been executed with four models of beam trawlers with. various prismatic coeffIcients and constant block

coefficient. In the past several accidents have occurred with beam trawlers travelling with high speed In a following sea. A temporary lack of stability on the crest of a following wave was assumed to be the cause of' some of these accidents. It becomes more and more important to have an idea of the change of

stability of a ship under way. At the last meeting of the international Fisheries Division at Berlin the necessity of special attention for the problem of the

stability of' small fishing boats has been stressed [i]. Criteria for the stability of ships applied in dff'erent countries have been reviewed in 2] and particu1arly for fishing vessels in

[3,1.

Most of these criteria are related to the zero speed situation of the ship.

Recently interesting experiments have been conducted by Ferguson and Conn to show the change of stability with speeds up to Fn

0.6

in still water for models with various block coefficients [5]. It appearect from these tests that

generally there is an increase of stability with a maximum at Fn = 0.12. It was also apparent that a downward movement of the bow can be associated with a gain and an upward movement with a decrease of the stability. The authors recommend to use the sinkage and trim results from the model tests as a first

indication of the change Ifl Stability with speed.

A theoretical method of calculating the righting moment of' a ship under way in still water with an initial angle of heel is proposed in

_[6]

from. which it was concluded that in practice a gain in the righting moment always arises for ships with full forms and this gain should increase with the block coefficient, while

for ships with fine forms this increase of the righting moment should be small or sometimes negative. The reduction of the stability of a ship under way in a sea has been treated by several authors [2, 3, ï, 8, 9, 10, ii].

Experiments concerning the stability of' a ship on the crest of a following wave

have beenreportedin [9,12,13] where a reduction of the righting arm up to 50%

is mentioned. Methods for the calculation of' the stability of a ship on the crest of a following wave have been given in [2,9,13,1i,1S] mostly including the important "Smith-effect't.

-2-For our case use has been made of the linearised "Smith-effect" according to

Paulling

_[9].

The ship is supposed to be in a static position with respect to

the wave, while the influence of speed, generating the ships own wave system,

is neglected. The phenomenon of the rr1w1 change of stability in a following sea causing a rolling motion and the effect of other mòtons on the stability

are not taken into account here.

Fishing boat designers of to-day prefer to use the prismatic coefficient rather than theblock coefficient to qualify the fineness of a boat [lE]. With respect to the resistance Traurig recommends a prismatic coefficient of

_0.575

for fishing boats in [16]. In the next sections the calculation and experimental procedure are presented which have been used in the present analysis. The results are compared with each other for the considered models and situations.

2. Calculations

2.1. General calculation method

The general method applIed here for the calculation of the transverse stability is an extension of the method developed by F. Taylor and published in [it].

Apart from normal ships the computerprogatn is suitable for

ships with level or uneven keel ships having s. trim angle

ships in a regular sine wave with a variable wave length and a variable

wave height while the position of the crest of the wave along the ship

is arbitrary.

2.2.Description of the general calculation method

The stability is calculated by- means of sectional area's and moments. For all waterlines yy (q) (see fig. i) is determined, beìng the distance from the

centre plane to the point of intersection ofthe inclined waterplane WL(i)

and the waterplane WL (q) in the upright position of the ship. The inclined waterplanes are rotated around a single axis in the centre plane which is

situated above the baseline at a distanceof one third of the breadth. This

arbitrary asuxnption keeps the distance between the waterlines independent of

the angle of heel, while the designed load waterplane cuts off a volume which

is fairly constant at all angles.

Fig. 1 Section with waterlines

-'t-For section r holds that the distance

from

the centre plane to the point of intersection of the inclined waterplane j and waterplane q is

yy ('i) yy (o) + Ay

Ay = a/tg 4) (i)

in which

a

= distance between the waterlines for section r From fig. i also follows

w(q) = y(q) - yy(q)

m(q) = {y(q) +yy(q)} (2)

The following conditions should be made

if w(q) 2y(q) take w(q) 2y(q) and m(q) O

and if w(q) o take w(q) = o and mtq) = yy(q)

(3)

If the above mentioned conditions are satisfied for all waterlines of a section the re-immersion problem, as illustrated in fig. 2, is automatically solved.

Fig. 2 Section with immersion

The area's and area-ioments of section

r

are for the inclining waterplane WL4)

as follows H

the area A (r) ₌

f

w(q) dz

the area-moment about the base line

(r) =

J

w(q) z (q) dz

(5)

w(q)

o

w(q) >0

w(q)

0

w(q) >0

w(q)

2y(q)

re -immersion

Immersion

and the area-moment about the centre plane

M(r) =

w(q) m (q) dz

₍₆₎

Longitudinal integration of area's and-moments of each section up to the inclined

watrplanes gives the volume and the volume-moments from which follow the

distances from the centroid of the vQlume to the baseline and the centre plane

respectively BZ and and hence (see fig. 3)

'1 sin = sin + cos

4

(î)

Fig. 3 Section with inclined waterline

The calculated results for the various beam trawlers in still water with zero speed

are shown in fig. ). and with dashed lines in fig.

7,

10 and 12. 2.3. The stability in a longitudinal wave

In waves the pressure increase is not linear with the waterdepth but exponential

because of the centrifugal accelerations of the rotating water particles in the

wave, this phenomenon is known as the "Smith-effect". From Bernoulli's law the pressure follows

p = pgz/L-1p

in which -z is the distance under water from the still waterline.

The velocity potential of a wave for infinite waterdepth is known as kz

ge

sin(kx-wt)

₍₉₎

in which Ca = wave amplitude

g = acceleration due to gravity

k

2rv wave number

X = wave length

w = circular wave frequency

Substitution of

₍₉₎

into

(8)

yields as total pressure in the wave

r kz

p =pg

_{1-z +}

Cae cos (kx - wt)

For t = O this pressure will be

kz

p =p

(-z +e cos kx)

Differentiation of (ii) towards -z gives a formulation of what may be considered

as an "effective specific gravity":

'y'(x) y (i - k e

k05

a

in which: y= p g

This effective specific gravity is strongly dependent on the longitudinal position (x) relative to the wave. Its dependence on the depth (z) is for a section

(given x) negligible if only the range of z between keel and water surface is considered. Thus, for a given section a modified hyth'ostatic pressure distribution is adopted, controlled by the effective specific gravity, taken from equation (12)at a z-value corresponding to the posiiioiothe centroid of

the section. So far, Paulling

_[9]

is followed. Contrary to Paullin however, presently a different approximation is made in the wave, any"ïhere above the still water surface. Here the regular hydrostatic _{pressure distribution is used,} It must be understood, that in any section in the crest of the wwe,thé above

mentioned centroid is taken at its stil]. water position. For each section the area's and area-moments of (14,

5, 6)

_{in paragraph 2.2.are corrected in such a}

way that area's and area-moments" are obtained, which are equal to

the area's and area-moments above the still water surface to which are added the area's and area-moments below the still water surface (or the actual waterline in the case of a wave trough) multipLipd byy' (x) (12).

-

T-(io)

Q

After integration over the sbip' length. of th.e sectional "effective area's and area-moments" the corrected volumes and yo1ume-mments re obtained from which the corrected values of (') follow for the case of a ship in a longitudinal wave.

The calculated values for the different beam trawlers with the crestamidships

are shown in fig. , 11 and 12.

3. Experiments

3.1Descrition of ship and models

The experiments have been carried out with a series of four models, derived from the modern Dutch beam traler IJM _{of which the prismatic coefficient}

IS

_{0.61.15 (model Iii). The models have all main dimensions in common (see table I),} but differ in the longitudinal prismatic _{coefficIent C and the midship section}

coefficient CM which has been varied in such a way that the blockcoefficient

C

CB remained constant : C =

p

As a consequence, stability characteristics _{and formparameters differ as shown} in table II. The scale ratio of the models is 15.

9

TABLE I _{ship models}

Length overall LOA

Length between perpendiculars L

Length C.W.L. _LCWL

Length over the

ordinates LORD Beam Depth amidships Draught forward (C.W.L.) Draught after (C.w.L.) Mean draught (C.w.L.) Volume of displacement

L.C.B. after L072

Centre of gravity above

the base line Radius of gyration for pitch Block coefficient CB 26.25 m 23.25 ni 23.15 m 22.80 m 6.1.io m 3.10 m 1.95rn 2.63 m 2.29 ni 1614.16 m3 0.615m 2.53 m O.2SLORD 0.148 1.150 m 1.551 m 1.51.13 m 1.520 ni 0.I27 m 0.201 m 0.130 m 0.115 ni 0.153 ni 0.048614 ni3

o.o4i

m 0.169 m O.2SLORD 0.148

The numbers between the brackets indicate the registration numbers of the models.

In the next sections only the length over the ordinates, LORD, will be taken into account. The position of the centre of gravity above the base line KG is chosen in accordance with the average results of rolling tests with the actual ship

for different loading conditions as published in [18]. The maximum speed of the vessel is free running 9-10 knots (Fn = 0.31 - 0.3k) and fishing about 14 knots

(Fn

0.114).

The models have been tested in three conditions viz. without bulwark, with closed bulwark and with open bulwark.

2 Measurin system

The models had been ¿onnected to the towing carriage by means of two guides at a distance of 0.5 m before and aft of the centre of gravity. This guiding

system had been adapted to the following requirements

freedom to heaves pitch, surge and roll of the model without suffering resisting forces or moments from the guides

resistance against sway and yaw while the average transverse force is kept zero by automatic control of the drifting angle.

Because of the heeling angle, the underwater hull shape is non-symmetrical,

which causes a transverse force and yawing moment with forward speed. In the

actual case of the ship this force is neutralized by the occurrence of drift,

while the yawing moment is counteracted by the rudder-action. This lastaspect has been neglected in the present test, while the transverse force, which must affect the heeling angle, has been accounted for, with the aid of the control system mentioned. The drifting angle was actuated by sideways shifting of the rear vertical guide which movement was controlled by two

force-transducers which form a part of the guides. 10 -TABLE II bi,p (LmI1++) Model I (iol) Model II (loo) Model III

(14)

Model IV

Metacentre above baseline 3.335m 0.209m 0.217m 0.222m 0.221m

Metacentre height 0.805m 0.01-fOOm O,0148m 0.053m O.058m

Halfangle of entrance waterline 31,5° 214.7° 28.1° 31.5e 35.0°

Midship section coefficient CM 0.71414 0.881 0.808 0.71414 0.691

Longitudinal prismatic coefficient C

p

These guides had been connected to the model by universal joints placed in line

with the model's centre of gravity. The initial heeling angle has been

achieved by the displacement of a weight p

(5,5

kg) over a distance b in transverse direction (see fig. 5)

In dynamic conditions the alteration of the heeling angle has been

determined by measuring the relative vertical displacement of two points in the

middle of the model at port- and starboard side. From these points a wire, stretched by a small weight at the end, had been conducted over a potentiometer. The

difference of the displacements of the two points was recorded on aU.V recorder together with the wave height and, as a check, the total transverse force.

3. 3.Experimental procedure

The expériments may be considered as heeling tests in still water without and

with speed and on the crest of a following wave. From fig. ₅ follows for the

case of still water and zero speed after shiftinga weight p over a distance b:

P sin4 pb cos4)

ï:in4)=-os=

'cos4)

(13)

with G' for the resulting centre of gravity

If the initial heeling angle 4) changes into 4) because of speed or wave, the false

metacentre N changes into N, while '

remains constant and consequently eq.13

will change into the next form

Fig 5

-

b

GN sin4)

-cos4)

= GG cos4)

(i1.)

Section in the case of a shifted load

With obtained from the static test and 4) measured, the resulting arm sin4)

is determined. The results for the four beam trawlers are shown in the figures 10 and 11. Curves of cos cp(see fig.6) stand for the heeling moments, while the curve stands for the recovering moment. When with increasing angle

of heel the recovering moment cannot surpass the heeling moment, the condition is unstable. In the case of the closed bulwark there will be a discontinuity

'cos

4)

Gisin

Fig. 6Heeling and recoverinnioment

The procedure. followed was to set the initial heeling angle at a round value in the static condition. With speed or wave, the altered angle was measured by the potentiometers. At first heeling tests up to 30 degrees have been

carried out in still water and with zero speed for the four models in two conditions viz, without bulwark and with closed bulwark. The results are shown in fig. ₇ for ach trawler seperately and in the case without bulwark for all trawlers together in fig. 13. Next the alteration of the initial

heeling angle5, 10, 15, 20, 25 and 30 degrees has been measured in still water for modeispeeds which were in accordance with ship speeds of 14, _{8 and}

12 knots (Fn = 0.1)1., 0.28 and. 0.142). These results are shown in fig. 8 and 9

for the four beam trawlers, where the relation is given between the altered

righting arm i sin and speed and the relation between the heeling angle

and speed. The curves of righting arms GN sin are shown in fig. 10 for each trawler seperately arid, in the case with open bulwark for all trawlers

together in fig. 13 with respect to one speed corresponding to a ship speed

of 10 knots (Fn = 0.314).

Finally the altératióna of the above mentioned initial heeling angles have been

measured in a following wave with wave length equal to model length and a

L

wave height 2Ca = /30 also for a modeispeed corresponding to a ship speed of 10 knots (Fn = 0.314).

th closed buLwark

-The curves of rigting arms GN sn ₄ are represented in fig. 11 for each trawler seperately in the case of the wave crest midships, while fig. 13 shows the same results for all trawlers with open bulwark together.

The period of encounter was kept very large to avoid a tuning effect because of

1. Results

To compare the calculated reduction of the static arms of stability in waves

with the experimental results, it appears to 'be necessary to eliminate the influence of the ship speed frani the experimental data. To this end, the stability arms,

obtained from the experiments in waves have been reduced with the results obtained

with speed in still water. Now it is supposed, that the influence of the wave only remains. This result added to the calculated arms of static stability

(no speed, no waves) should produce the experimental data which are comparable

to the calculated values. A comparison is shown in fig. 12 for the case of a ship speed of 10 knots and a following wave of X=L and 2C L130 with wave

crest midships.

It might be important to see how the initial heeling angle in the case of a constant load shift is changed because of speed and waves. For this purpose the measured heeling angles in still water and in a following wave (crest

midships) both for a ship speed of 10 knots relative to the initial heeling

angle are represented in fig. 1 for all models with open bulwark together.

For the models without bulwark and the heeling anglesof 10, 15, 20 and 25

degrees the following curves of the righting arms as a function of the prismatic coefficient are shown in fig. 15:

the experimental results in still water for a ship speed of 10 knots and the calculated ones for zero speed.

the experimental results in a following wave (crest midships,X L, 2C=L/30)

for a ship speed of 10 knots and the calculated values for the same wave and speed zero.

the experimental results in still water for speed zero and those for a

ship speed of 10 knots and the experimental results in a following wave (crest midships, X= L,

5. Discussion of results

For still water and zero speed it ppers from the celculations (fig.

)

and the

experiments (fig. 13), that the static

_{arm of stability for every heeling angle}

increases with the prismatic coefficient, although the experimental results

show less difference between model II

_{nd III than those calculated. In the}

_case

of speed, both in still water and in the crest of a following wave, it is

evident from fig. 13, that there is almost

_{no difference left between the}

righting arms of model II and III with

_{open bulwark, The models without bulwark}

show the saine tendency as becomes apparent

_{from fig. 15 again with almost no}

difference between the experimental results

_{of model II and III, which is}

contrary to the calculated results.

From fig. 15 it is also evident, that in

_{general, there is a small gain of}

stability in still water because of speed, but that a larger loss occurs in the

crest of a following wave. Starting from

_{a constant load shift it is obvious}

from fig.

iIi, that for still water

_{the heeling angle is reducing with speed}

and also with a decrease of the prismatic coefficient, while this heeling

angle is increasing with the prismatic coefficient in

_{the crest of a following}

wave for a ship speed of 10 knots.

The figures 12 show, that model IV with the

_{fullest ends yields the best}

correlation between experiment and computation. This is

_{the case in which the}

speed influence on the stability in still water

_{was found to be small. In the}

case of model I, with the fines ends, the largest speed influence in still

water had been accounted for and in this

case the computed and measured arms

differ the largest amount. And so it appears, that in general the experimental

reduction of the righting arm because of the position

_{of the model on the}

crest of a following wave is smaller then the calculated one and this deviation

is increasing with a decrease of the prismatic coefficient or what comes to the

saine thing with the speed influence on the righting

_{arm in still water; it is}

therefore reasonable to accept the possibility,

_{that the speed influence on the}

stability is highly dependent on the

Wayep

-6. Conclusions

The experiments show that in stil]. water the arms of static stabilitr increase

with speed and with a decrease of the prismatic coefficient, but a larger

reduction was found because of the position of the ship in the crest of a

following wave (À=L, 2

jJ30)

in the case of a ship speed of 10 knots

(Fn = 0.3)4). However, this redution appears to be smaller than the calculated one, except for model IV with a prismatic coefficient of 0.695, where a good agreement appears to exist between experiment and calculation. This deviation is also increasing with a decrease of the prismatic coefficient just like the speed influence in still water. Both for still water with speed and in the crest of a following wave little difference was found between the curves of righting

arms of model II and model III with a prismatic coefficient of respectively

0.595 and 0.6)45.

-Nomenclature

A sectional area

B centre of buoyancy

CB block coefficient

CM midship section coefficient

longitudinal prismatic coefficient metacentre height

false metacentre height

H maximum draught

centre of gravity above baseline (K) false metacentre above baseline (K) L length of' model or ship

LCB longitudinal centre of buoyancy LCWL length of construction waterline LOA length overall

length over ordinates

M metacentre

Mb moment of the sectional area about the baseline

M moment of the sectional area about the centreplane

N fais metacentre

WL waterline

g acceleration due to gravity j jndex of inclined waterlines

wave number

p pressures inclining weight

q jndex of waterlines in the upright position of the ship

r index of section

t time

xyz right hand. coordinate system fixed in ship with z positive upwards

-r specific gravity of water

X wave length

Ca wave amplitude

angle of heel, velocity potential of a wave

p density of water

circular wave frequency

-References

0. Greger

Gedanken zum Stabilittsproblem kleiner FLschereifahrzeuge

Schiff und Hafen, Heft 3/1910,22 Jahrgang. J. Punt

De stabilitejt van een kustvaartuig van het gladdektype in langsscheepse golven. Schip en Werf 33e jaargang no, 11 en 12/1966.

K.Th. Braun

Die Stabilitatsfrage bei Fischereifahrzeugen. Schiffbauforschung t _1/2/1965

L. J.G. de Wit

Report on the problems of the stability required by fishing vessels.

FAO/60/L/8565-R.p Bebr. 1961

A.M. Ferguson, J.F.C. Conn,

The effect of forward motion on the transverse stability of a displacement vessel.

Transactions of the Institution of Engineers and Shipbuilders in Scotland

1969-1910; vol. 113, part 5, pp. 215-262

G.V. Sobolef, V.B. Obraztsof

Calculating the righting moment of a ship under way with an initial angle of heel. (in Russian)

Trans. Leningrad Shipbuild. Inst. no. 63 (1969)p.61.

K. Wendel

Stabilit.tseinbussen im Seegang und durch Xokdecklast. Hansa 1951f

cpp.

2016-2022

0. Stanvaag, A. Gorberg

Transverse Stability of whalers when in longitudinal waves. Trondheim Ship Model Tank, Report no. 26, Dec. 1953

J.R. Paulling

The transverse stability of a ship in a longitudinal seaway.

Journal of Ship Research vol. 1, no. pp. 37_I9. march 1961. 0. Grim

Rolischwingungen, Stabilitat und Sicherheit im Seegang.

Schiffstechnjek Heft 1, 1952 pp. 10-21.

0. Grim

Beitrag zu dem Problem der Sicherheit des Schiffes im Seegang.

Wissenschaftliche Zeitschrift der Universitat Rostock-lO Jahrgang 1961.

-W. Graff and E. Heckscher

Widerstands- und Stbilit.tsyersuche mit drei Fschda.mpferinodellen. Werft-Reederei-Hafen, vol. 22, 191+1, pp. 115120.

B. Arndt and S. Rodin

Stabilitat bei vor- und achterlichem Seegang. Schiffstechnik Bd.

5 -1958.-Heft 29, pp. 192-199

114. E. Upahi

Betrachtung t1berStabilit.tsverfahren im Seegang.

E. Upahi

Rechnerische Berilcksichtigung des Smith-Effektes. Schifbautechn±k 10 -

₁₉₆₀

H-1, pp. 21-28

J.O. Traung

Fisheries and Nava1''rchitecture.

FAO Fisheries 1ulletin, Vol. VIII,]c.14,

Oct. -

Dec.

_1955.

F. Taylor

Computer applications to shipbuilding. R.I.N.A. Paper No. 6 May

1962.

F. de Beer

Metacentric height and rolling period.

I.S.P. vol. 17.

Febr.

1970 -

No.

186.

Schiffbautechnik 11 -

9/1961

p.p.

14141 - 141+6

11 -10/1961

p.p. 510 - 5114

o

List of figures

Fig. i Section with waterlines

Fig. 2 Section with immersion

Fig. 3 Section with inclined waterline

Fig. ) Calculated static arms for all models together

Fig. 5 Section in the case of a shifted load

Fig. 6 Heeling and recovering moment

Fig. 7 Static arm in still water for zero speed

Fig. 8 Righting arm and heeling angle dependent on speed for models without

and with closed bulwark at constant load shift

Fig. 9 Righting arm and heeling angle dependent on speed for models with

open bulwark at constant load shift

Fig.10 Static arm in still water for a ship speed of 10 knots Fig.11 Ctatic arinon the crest of a following wave

Fig.12 Static arm on the crest of a following wave determined with calculated

and experimental reduction for waves

Fig.13 Static arms from experiments for all models together

Fig.114 Heeling angle in relation to the initial heeling angle for constant load shift

LO

(D10

CALCULATION FOR MODELS WITHOUT BULWARK IN STILL WATER. V=0

-

MODEL I (101) Cp= .545 11 (100) Cp=.595 11E (98)

Cp .645

]

(99)

Cp.695

r

15 20 - DEGREES

CALCULATION FOR MODELS WITHOUT BULWARK

IN WAVES. V=O

WAVE CREST MIDSHIPS

X =:L

= L/30

MODEL

10 15 20

- DEGREES

Fig. 1 Calculated static arms for all models together

5 10 25 30 O 5 g 30

Q-X

u,

o

Li LO E o

f

30

a-z

u) Ö Li C

z

(D10

25 30

g E u LO 0 ¿.0 10 O o

UNSTABLE POSITION BULWAJ( LR4R WATER

M0DEL (98) Cp= .645 STILL WATER. CALCULATION WITHOUT BULWARK

EXPERIMENT WITHO(J BULWARK

-

EXPERIMENT WITH CLOSED BULWARK

. UNSTABLE POSITION

7,

5 10 15 20

4' -

DEGRE 25 30 a-X u, 10 _.. UNSTABLE POSITION 20-e C V' o 10 15 20 G - DEGREES

-30 TER 25 30 4' DEGREES

MODEL (99) Cp =695 STILL WATER.

VO LJLW8JA(

40

CALCULATION WITHOUT BULWARK

o o EXPERIMENT WITHOUT BULWARK

,.41)NDFRWATFR

- ._.

_. EXPERIMENT WITH CLOSED BULWARK vO

UNSTABLE POSITION

V

E

V

30

---

Q-X Il) e 20 C w 10 O

MODELl (101) Cp.5L5 STILL WATER.

CALCULATION WITHOUT BULWARK

EXPERIMENT WITHOUT BULWARK

EXPERIMENT WITH CLOSED BULWARK v=O

MODEL (100) Cp .595 STILL WATER.

- - - -

CALCULATION WITHOUT BULWARK

- o o EXPERIMENT WITHOUT BULWARK

_v0

UL8

R WATER

40 EXPERIMENT WITH CLOSED BULWARK

f 30-

V

25 10 15 20

V

ß'

30 30 25

V

7,

g 10 15 20 4' DEGREES 5 o

(D. e C E ¿o -0° 25° 120° 15° O 10°_ G 5° I I . I

MODEL I (101) Cp.545 - STILL WATER

EXPERIMENT WITHOUT BULWARK EXPERIMENT WITH CLOSED BULWARK

.-_-. - .

30°

-

25° -Ui Ui - 0 L

MODELt (98) Cp.645 STILL WATER

-oo--- EXPERIMENT WITHOUT BULWARK EXPERIMENT WITH CLOSED BULWARK

4

UNSTABLE POSITION LO -- 25° 120° 30 u, W Ui o w o -e LO n-20 E e C lo 5 10

SHIP SPEED KNOTS

ioo- _:

O O

O

o

SHIP SPEED - KNOTS

MODEL (99) Cp .695 - STILL WATER

_o-__. EXPERIMENT WITHOUT BULWARK

EXPERIMENT WITH CLOSED BULWARK

4

UNSTABLE POSITION LO

-

.__- 25° 3° 10 5 10

SHIP SPEED KNOTS H c+. ç) H O (D p, ,-p, (D (D !-' F-" (D (D U) o

-

e--10- O O o o e Q. 5 10 SHIP SPEED ç) o O U) ci-p, O c-t-H O P) P Ci) H . p (D O - c-i-O . Cfl d. (D (D O Fi O (D H Cn

-u) O u 40 E

MODELI (100) Cp° .595 - STILL WATER

EXPERIMENT WITHOUT BULWARK

EXPERIMENT WITH CLOSED BULWARK UNSTALE POSITIÖN 40 -

-

40-.__-.A-- 25° E

2______________.. 15° -o u-e w= O 0 010° 10-O O 0 5° o 0 5 10

SHIP SPEED KNOTS

5 10

KNOTS SHIP SPEED KNOTS

5 lo 0 5 10

SHIP SPEED KNOTS SHIP SPEED KNOTS

10 o H H c-t. Q H. Ott (D (D C: o o o c-t. (D (D o O Ott c+ t.-(D o p o (D (D (D Cn o

-H (D

FI) c c-tfl o O Lo lo

SHIP SPEED - KNOTS

Cn

(D

(D

3O-_

-20 _-_. -- -O--15

MODELI (98) Cp o.6L5 STILL WATER

-IJ---{J- EXPERIMENT WITH OPEN BULWARK

.. ___.._.._.D- 2 MODELE (1

-D--a-LO

-D

«0--0-- -0- 20

MODEL 99) Cp -a--..-O- EXPERIME

00) Cp o.595 STILL WATER

EXPERIMENT WITH OPEN BULWARK UNSTABLE POSmON LO 30

-2''

0--... .. -.0-._

f II 10 LO 30

10

o .695 STILL WATER

NT WITH OPEN BULWARK

."DS 40 E '3 3O- 2O- u-R

'alO-o 1) EXPERIMENT (.n u.! t Cp 60 30 ,10 o z u, o u-e_C 03 LO 3(1 IO MODEL

-G-..-u-.--.:

I (1 20° 150 T t .565 STILL WATER

WITH OPEN BULWARK

- S--0--..

_-oN.

-20.._..

O

-

---0-0 5 10 5 10 5 10 o s io

SHIP SPEED KNOTS SHIP SPEED - KNOTS SHIP SPEED KNOTS. SHIP SPEED. KNOTS

5 10

SHIP SPEED - KNOTS

0 5 10

SI-IIP.SPEED KNOTS

10

SHIP SPEED KNOTS

3c g 20 o L& e C 10 o O

MODEL I (101) Cp.5L5 STILL WATER

o

10 0 -15 20° 20 25° 30° INITIAL HL 30° INITIAL HEEL -O 20° INITIAL HEEL 5 10 15 20 DEGREES 25 30 LO

j:

10 o O E 30 20 e C u, 10 5. 10°

r

r

15°

7

7

r

r

>Vo1O KNOTS -BULWARK UNDER WATER ,°INITIAL HEEL 30° INITIAL HEEL ,"25° -i _30°INITIAL HEEL 2Ot'.. 25°

2q-MODEL (99) Cp r 695 STILL WATER

_____CALCULATION WITHOUT BULWARK FOR VoO

EXPERIMENT WITHOUT BULWARK

\

LO - EXPERIMENT WITH CLOSED BULWARK Vo1O KNOTS

EXPERIMENT WÌTH OPEN BULWARK i

UNSTABLE POSITION ,,A?25° INITIAL HEEL

.7

25°INITIAL HEEL - 20 _20°

-5

r

10 10 15 20 DEGREES 15° 25 20°INITIAL HEEL 30

CALCULATION WITHOUT BULWARK FOR Vro

EXPERIMENT WITHOUT BULWAR<

LO EXPERIMENT WITH CLOSED BULWARK >VlO KNOTS BULWARK UNDER WATER

EXPERIMENT WiTH OPEN BULWARK

i

._._.

UNSTABLE POSITION

30 INITIAL HEEL.

O 5 lo is 20 25 30

DEGREES MODEL (98) Cp .645 STILL WATER

CALCULATION WITHOUT BULWARK FOR V00

o o EXPERIMENT WITHOUT BULWARK ',

-

EXPERIMENT WITH CLOSED BULWARK >Vr1O KNOTS ¡ BULWAR}(

EXPERIMENT WITH OPEN BULWARK i .'° UNDER WATER

-H UNSTABLE POSITION _{INITIAL HEEL}

7-20'

_NITIL HEEL

Vo O

MODEL U (1OÒ). Cpr .595 STILL WATER

- - -

CALCULATION WITHOUT BULWARK FOR

EXPERIMENT WITHOUT BULWARK

.__ EXPERIMENT, WITH CLOSED BULWARK

EXPERIMENT WITH OPEN BULWARK UNSTABLE POSITIÖN

7,

lo 15 20 DEGREES 5 25 30 LO E

30

20 U-e C 10

cI p, H' Ç, p, FI o C-t (D Ç, 'I (D Ci) o F-b F-b o ¿0 o o Q-X (n 20 u-e C 10 I I I ¡ MODEL .1 (101) Cp.545 IN WAVES

CALCULATiON WITHOUT BULWARK FOR VrO

.._.

EXPERIMENT WITHOUT BULWARK

'

EXPERIMENT WITH CLO BULWARK >Vrl0 KNOTS

. - EXPERIMENT WITH OPEN BULWARK

UNSTABLE POSITION

WAVE CREST MID9IIPS

XrL 2a rL,30 25 INITIAL HEEL _..!ÇINITIAL HEEL 25 INITIAL HEEL 5

V

l5 20 INITIAL HEEL

V

_{20 INIlAL HEEL} LO 30 20 10 O 20 u-e C In lo O I I I MODEL E (100) Cp .595 IN WAVES

CALCULATION WITHOUT BULWARK FOR VO

--o-- EXPERIMENT WITHOUT BULWARK

-

. EXPERIMENT WITH CLOSED BULWARK >V riO KNOTS

EXPERIMENT WITH OPEN BULWARK )

UNSTABLE POSITiON

WAVE CREST MIDSHIPS

AL

2r L,

.1 A0INITIAL HEEL 'ÑrnALEEL O1INITIAL HEEI I I INITIAL HEEL

iL

°INITIAL ÑL J I o - DEGREES - DEGREES H' I I.

--

I

-I

I

HObEL ]It (98) Cp = .6L5 IN WAVES MODEL (99) Cp r .695 IN WAVES

CALCULATiON WiTHOUT BU1WFRK FOR VrO CALCULATIÓN WITHOUT BULWARK FOR VrO

o-_-o-- EXPERIMENT WITHOUT BULWARK

'

EXPERIMENT WITHOUT BULWARK

'

CD Lo - EXPERIMENT WITH CLOSED BULWARK V = 10 KNOTS LO - . EXPERIMENT WITH CLOSED BULWARK >V riD KNOTS

EXPERIMENT WITH OPEN BULWARK ) EXPERIMENT WITH OPEN BULWARK )

UNSTABLE POSITION UNSTALE POSITION

WAVE CREST MIDSHIPS WAVE CREST MIDSHIPS

ÀL

E ArL

2o. INITIAL HEEL _{3O -} rL/3O

10 15 20 25 30 o 5 10 15 20 25 30 DEGREES DEGREES 5 lo 15 20 25 30 o 5 lo 15 20 25 30 30 X u, 20 e C lo o-. X (n e e C w

Q r) H p (D p (D k (D (D H (D r) o. o p) (D (I) 40 LO u, 20 e C In 10 o o I I I I

MODEL I (101) Cp .545 WITHOUT BULWARK IN STILL WATER AND IN WAVES

CALCULATION FOR V=0 IN STILL WATER

CALCULATION FOR VnO IN SuLL WATER WITH CALCULATED REDUCTION FOR WAVES

._. CALCULATION FOR VnO IN SuLL WATER

WITH EXPERIMENTAL REDUCTION FOR WAVES

WAVE CREST > MIDSHIPS

)

2a L130

I I I

MODEL1 (98) Cpn .645 WITHOUT BULWARK IN STIL

CALCULATION FOR V0 IN STILL WATER

CALCULATION FOR VnO IN STILL WATER

WITH CALCULATED REDUCTION FOR WAVES

--o--o.-- CALCULATION FOR V=O IN STILL WATER

WITH EXPERIMENTAL REDUCTION FOR WAVES

WAVE CREST > MIDSHIPS

)L'

'30 5 10 15 20 DEGREES 10 15 20 DEGREES 25 E. e C In a-X, u, 20 10 E-u LO 30 Q-X u, o u-20 e C In 10 o 5 10 15 20 DEGREES 10 15 20 - DEGREES WAVE CREST MIDSHIPS

)

_{2a L30} ¡ I I

MODEL (99) Cp =695 WITHOUT BULWARK IN STILL WATER AND IÑ WAVES

CALCULATION FOR V=O IN STILL WATER CALCULATION FOR V=O IN STILL WATER

-

WITH CALCULATED REDUCTION FOR WAVES

O_ CALCULATION_{WITH EXPERIMENTAL REDUCTIOÑ FOR WAVES}FOR VnO IN STILL WATER

WAVE CREST

>.MIDSHIPS _r'

) X=L

-2a

I I T I

MODEL Z (100) Cp = .595 WITHOUT BULWARK IN STILL WATER AND IN WAVES

CALCULATION FOR. V=0 IN STILL WATER

CALCULATÌoN FOR V O IN STILL WATER

LO - WITH CALCUL TED REDUCTION FOR WAVES

CALCULATION FOR V=O IN STILL WATER

WITH EXPERIMENTAL REDUCTION FOR WAVES

25. 30 25 30 O 25 -30 20 u-e C 10

40 o 40 E

v0

20 u-lOE O -I UNSTABLE POSITION EXPERIMENT

MODELS WITH OPEN BULWARK IN STILL WATER V=10 KNOTS

MODEL I (101) Cp= .545 (100) Cp=.595 ]IE (98) Cp= 645 _o (.99) Cp=.695 -I UNSTABLE POSITION EXPERIMENT

MODELS W!T4-I OPEN BULWARK IN WAVES V=10 KNOTS

MODEL I (101) Cp= .545

-

ir (100) Cp=.595 lIt (98) Cp.645

(99) Cp.695

-I UNSTABLE POSITION

- WAVE CREST MIDSHIPS

XL

2a L/30

O 5 10 15 20 25 30

4' -

DEGREES

Fig.13 Static ar:s fron experiments for ail niodeistogetlier

EXPERIMENT

MODELS WITHOUT BULWARK IN STILL WATER V = O

MODEL I (101) Cp = .545 40 11 (100) Cp .595 11t(98) Cp=645 ]Z(99) Cp=.695 O 5 10 15 20 25 30 - DEGREES E

,30

0 u, 20

e

O) z (b ₁₀ -I 1 25 30 10 15 20 1) --- DEGREES

30 w w (D w ¡ e 20 10 MODEL N

MODELS WITH OPEN B

V= 10 KNOTS

-I UNSTABLE

O o

P'±g.11i Ileeling angle in relation to the initial heeling angle for constant load shift

-o 10 20 O 10 20

E 'I D-X U) 10 X E

e

C

z

(DO as D-X U) 20 X o

u-e

C w Z Io 10 05

MODEI.S WITHOUT BULWARK

IN. STILL WATER

MODELl E u a-20 X E

e

_C

z

(D 10 0.5 0.6 EXPERIMENT V=10 KNOTS CALCULATION V O EXPERIMENTS E u X U' 20 X o Li

e

C (A

z

(D 10 0.5 06

Cp-0.7 Cp 0.7 0.6 0.7 0.5 O.6 0.7

Cp -

EXPERIMENTS IN SILL WATER

a V1OKNOTSEXPERIMENTS

X= L, 2L/30

IN WAVE (CREST MIDSHIPS)

0.6

Cp

-0.6 Cp

IN - WAVES (CREST MIDSHIPS)

E u Q-20 X o u-e C Dt Z 0 10 07 0.5 06 O EXPERIMENT V =10 KNOTS O CALCULATION V = O 0.7 X=L , 2a L/30 07

Cp

-(D H E 1., û-X U' 20 U) _2G X X E

e

4»20 E

_e

C w I MODELl

I

I

N

C 10 (D 10 07 0.5 0.5 Cp 0.7 05

Cp

-E u

120

10 (D 05 05

Cp -

0.7