# principles of ship’s stability

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Principles of ShipsStability

PETRAS PIKSRYS

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SHIPS STABILITY

SHIPS STABILITY IS

THE TENDENCY OFSHIP TO ROTARE ONE

WAY OR THE OTHER

WHEN FORCIBLY

INCLINED

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WHAY IS STABILITY IS SO

IMPORTENT ?

IF THE SHIP LOST STABILITY WHAT

WILL BE HAPPENED:

1. LOST OF MOBILE

2. LOST THE HUMANS LIFES

3. LOST THE SHIP

4. LOST THE CARGO

5. OIL POLLUTION

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FUNDAMENTALS OF STABILITY

STABI LI TY is the tendency of vessel to rotate one way or the

other when forcibly incl ined.

IMPORTENT !!

Ships stability cant catch directly

Stability can define only by calculating

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HOW CALCULATING SHIPS

STABILITY AND CARCO PLAN ?

1.By previous similar cargo plan.

2.By standard cargo plan accordingSTABILITY BOOKLET

3.By standard cargo plan forms

4.By special cargo plan computer

5.By standard PC with special cargo

plan program 6.By special or standard hand

calculator

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SHIPS STABILITY CRITERIAS

THERE ARE TWO SHIPS STABILITYCRITERIAS:

1 h>0 ships metacenter height alwayspositive.

2 Zg < Zcritical

h = ZmZg

Zg defined by calculating

Zm define according hydrostatic curves

Zg critical define according specialdiagram.

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SHIPS STABILITY CALCULATING

SHIPS STABILITY CALCULATING BYMOMENT FORMULAS.

MAIN OBJECT OF CALCULATING TO

DEFINE SHIPS STABILITY CRITERIAS:

GM=h METACENTER HEIGHT Zg SHIPS GRAVITY HEIGHT

MOMENT FORMULA:

D0Z0+P1Z1+P2Z2+.+PnZn

Zg=

D0 + P1 +P2 + .. + Pn

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SHIPS STABILITY CALCULATING

Zg critical CURVE

8000 10000 12000 14000 16000 18000 20000

6.10

6.20

6.30

6.40

6.50

6.60

Zg critical

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WHO CALCULATING SHIPS

CARGO PLAN AND STABILITY? 1.CARGO OFFICER (ch.mate)

2.PORT CARGO OFFICER (supercargo)

3.SHIP

S MASTER

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SHIPS STABILITY

STABILITY

INITIAL OVERALL DYNAMIC

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STABILITY

INITIAL STABILITY- The stability of a ship

in the range from 0

to 7

/10

of

inclination.

OVERALL STABILITY- A general measure of a

ship's ability to resist capsizing in a

DYNAMIC STABILITY- The work done in heeling

a ship to a given angle of heel.

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INITIAL SHIPS STABILITY

Initial ships stability when ship inclinating

from 7 till12 degrees. Ships underwaterbody did not change volume

V0=V1

C

C1G

m

V0

V1

w L

W1

L1

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INITIAL METACENTRIC

FORMULA

m

G

C

M=D h sin Q

Qst

h

DVg

C1

lst

M=D lst

lst=hsinQ

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SHIPS STABILITY

CALCULATING Initial stability calculating by ships

stability triangle

Calculating formula lst= h sinQ

Overall stability calculating byhydrostatic ships body formulalf

Dynamic stability is the area underthe static stability curve

Dynamic stability also potentialenergy available to return the ship tothe upringing

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STABILITY TRIANGLE

Q

m

C

G

C1

lst=hsin Q

l sth

D

Vg

lf

l f

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4000 6000 8000 10000 1200014000

1600018000

2000

0.4

0.8

1.2

1.6

2.4

2.8

10

20

30

40

50

60

70

80 90

PHANTACORENS

SHIPS BADY FORM STABILITY ARMS lf

lf

DISPLACEMENT

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METACENTRIC HEIGHT

Metacentric height GM is calculated by subtracting KG

From KM (GM=KM-KG), GM is a measure of the ship.sstability. KM=h.

With initial stability(0 10 deg.) the metacenter does not

move, and Sine function is almost linear(a straight line).

Therefore, the size of the ship,s Righting Arm, GZ, isdirectly prportional to the size of the ships Metacentric

Height, GM.

IMPORTENT !

Thus , GM is a good measure of the ships

initial stability.

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METACENTRIC HEIGHT

m

G

C

h

a

WL

a

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MAIN STABILITY POINTS

There are three main stabilitypoints:

m- metacenter is the end ofhydrostatic force when shiplisting.

G- centre of ship gravity

C- centre of ship underwaterbody.

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SHIPS STABILITY

STABILITY REFERENCE POINTS

G

h

a

r

C

WO Lo

m

Zc

ZG

Zm

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MAIN STABILITY POINTS

m metacenter G center of gravity

C center of buoyancy

m

G

h

a

C1

Q

Wo LO

W1

L1

Q

C

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SHIPS STABILITY

METACENTER

m

C0

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SHIPS STABILITY

METACENTRIC HEIGHT FORMULAS

h=r-a

h=zmzG

h=zc - ro - zG

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METACENTRIC HEIGHT METACENTRIC HEIGHT MEENS SHIPS INITIAL STABILITY

m

G

C

h

a

Wr0

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Three statesof static equilibrium

(a) Positive stability - m above G

(b) Neutral stability m and G in

the same position

( c )Negative stabilitym below G

m

a

m G

b

G

mG

h>O h=O h

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POSITIVE SHIPS STABILITY

Positive ships stability when m above G

h>0

C C1

G

mh

W L

W1

L1

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SHIPS STABILITY CURVE

L

l st

Q

h57, 3

Q

POSITIVE SHIPS STABILITY

h>0

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NEUTRAL SHIPS STABILITY

Neutral ships stability when m and

G in the same position

h=0

C C1

G m

WL

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SHIPS STABILITY

NEUTRAL SHIPS STABILITY

lst

Q

h=0

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NEGATIVE SHIPS STABILITY

Negative ships stability when m

below G

h

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h=-0

NEGATIVE SHIP S STABILITY

57.3

-h

Mst

Qst

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STABILITY CONDITIONS

The positions of Gravity and the Metacenter will indicate the initial stability

of a ship.Following damage, the ship will assume one of the following three stability

conditions:

1. POSITIVE STABILITY. The metacenter is located above

the ships center of gravity.

As the ship is inclined, Righting Arm are created which tendto return the ship to its original, vertical position.

2. NEUTRAL STABILITY. The metacenter and the ships

center of gravity are in the same location. As the ship is inclined,

. there are no returing moment.

3. NEGATIVE STABILITY.The ship,s center of gravity is

above the metacenter.

As the ship is inclined, negative Righting Arms (called upsetting

arms) are created which tend to capsize the ship.

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METACENTRIC FORMULA

h=Zm- ZG

CC1

m

h

lst

M=( lflst)D

OVERALL

Vg

W0 L0

W1

L1

lf

G

Zm ZG

M- UPSERTING MOMENT

M

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METACENTRIC HIGHT

METACENTRIC HIGHT IS FIRST DERIVATIVE SHIPS

STABILITY CURVE

h

57,3

Mst

Q

lst

METACENTER HEIGHT

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METACENTER HEIGHT

W L

W1

L1

C

C1

G

m

h

Metacenter height GM is a determine of shipstability curve

METACENTER MOMENT IS UPSERTING MOMENT

M= D h sin Q

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W L

DYNAMIC STABILITY

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SHIPS DYNAMIC STABILITY

DYMAMIC MOMENT

Q

M

M DYNAMIC

MOMENT

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SHIPS STABILITY

STATIC MOMENT CURVE

Q

M

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SHIPS DYNAMIC STABILITY

MAXIMUM DYNAMIC ANGLE

Q dynQ static Q

M

Qdyn max

S1

S2

Qdyn WHEN S1= S2

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SHIPS DYNAMIC CURVE

SHIPS DYNAMIC STABILITY CURVES APPLICATES

IS EQUVALENT STATIC CURVES AREA

Mdyn

S=Mdyn

Q

Mdyn

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DYNAMIC STABILITY

The dynamic stability is the area under the curve in metre-radians

Multiplated by the ship,s displacement in tonnes. It is areas underthe GZ

Curve which are required for checking stability criteria which

depending

Upon the ship,s data may be expressed in metre-degrees or

The area unde GZ curve also the potential energy available to

return the

Ship to the upringht.

Principle of conservation of energy, the potential energy

in converted into

Rotation energy as the ship moves towards the upright.

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Md

Mst

Q max

DYNAMIC STABILITY

Mst

Q

Mdin

CURVE

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STABILITY ELEMENTS

THE LAW OF BUOYANCY

THE LAW OF GRAVITYSTABILITY REFERENCE POINTS

LINEAR MESURMENTS IN STABILITY

THE STABILITY TRIANGLE

RIGHTING MOMENT

STATIC STABILITY CURVE

DYNAMIC STABILITY CURVE

ROLLING PERIOD

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Learning Objectives

Comprehend the concepts of hydrostatics, buoyancy,

and Archimedes' principle

Comprehend static equilibrium of a floating vessel and

the relationship of the centers of gravity and buoyancyto righting arms and stability

Comprehend and identify positive, negative and

neutral conditions of stability

Comprehend the effects of movements of the centers ofgravity and buoyancy on vessel stability

Know how ship's stability curves are derived and

comprehend their use in determining stability condition

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Draft

Freeboard

Depth of hull Reserve buoyancy

List / Trim

Definitions

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SHIPS HULL MARKINGS

t XVIII hundred one Englishman called

PLIMSOL in Great Britan Parlament filds

for marcks on the hull to for Safe shipping.

Now thats marks called PLIMSOL MARKS.

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PLIMSOL DISC

PLIMSOL DISC DIVAIDING SHIPS

BODY IN TWO PARTS:

1. RESERVE BUOYANCY

2. DISPLACEMENT

W L RESERVE BOYANCY

DISPLACEMENT

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FREE BOARD

SHIPS MAIN FREE BOARD MEENS SHIPSRESERVE BUOYANCY

DRAFT

SHIPS MAIN DRAFT MEENS SHIPS

DISPLACEMENT

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RESERVE BUOYANCY

MAINTAIN FREEBOARDRASERVE

BUOYANCY PRIOR TO PREVENT

LIMITING DRAFTS ARE ASSIGNED

TOEXCESIVE HULL STRESS AS A

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FREE BOARD

WL

FREE BOARD

WNA

W

SF

TF

FREE BOARD MEENS RESERVE BUOYANCY

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DRAFT

MAIN DRAFT MEENS SHIPS DISPLACEMENT

W L

DRAFT

B

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Archimedes' principle

Calculations of displacement (W)

The effect of salt water and fresh wateron displacement (relate to draft)

[1/35 vs 1/36]

Buoyancy

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Archimedes principle

BOY D

A body immersed (or floating) in water will

buoyed

ARCHIMEDES FORCE

By a force equal to the weight of the water

displaced.

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THE LAWS OF BUOYANCY

1. Floatating objects posses the property of buoyancy.

2. A floatating body displaces a volume of water equal in

a body immersed (or floating) in water will be duoyed

up by a force equal to the weight of the water displaced

W L

C

Vg

D

G

D=Vg

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SHIPS BUOYANCY D=V*g

V*g

DG

C

WL

ARCHIMEDES FORCE

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WNAW

ST

F

TF

Markings of minimum allowable freeboard for registred cargo-

Carryng ships.Located amidships on both the port and starboard

sides the ship.Since the required minimum freeboard varies with water density

and severity of weather, different markings are used for:

- TF

Tropical Fresh Water- F - Fresh Water

- T - Tropical Water (sea water)

- S - Standard Summer

- W - Winter

- WNA-Winter North Atlantic

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SHIPS HULL MARKINGS

Calculative Draft Marks

Used for determining displacement and other properties

of the ship for stability and damage control.

Those draft marks indicate the depth of the keel (baseline)

below the waterline.

TWO POSIBLE MARKING SYSTEMS:

1. Roman numerals in height

2. Arabic numerals in height

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DRAFT IN FEETS

1 ft = 0.3048 m

XIII

XIV

XV

XVIXVII

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DRAFT IN METRES

1 ft = 0.3048 m

36

38

40

42

44

SHIPS HULL MARKINGS

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SHIPS HULL MARKINGS

These draft marks include the depth of any

projections below the keel of the ship.

Limiting Draft Marks

Limiting drafts are assigned to maintain

reserve buoyancy (freeboard) prior to

DISPLACEMENT

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DISPLACEMENT

The weight of the volume of water that is displaced by the

underwater portion of the hull is equal to the

weight of the ships

GRAVITYThe force of gravity acts vertically downward through the ships centerOf gravity. The magnitude of the force depends on the ships total weight.

MOMENTThe endency of a force to produce a rotation about a pivot point.This works like a torque wrench acting on a bolt.

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DISPLACEMENT

D=DLS + DS + DC

D Displacement

DLSWeight light ship

DS - Weight supply

DC - Weight cargo

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GRAVITY

THE FORCE OF GRAVITY ACTS VERTICALY

DOWNWARD THROUGHT THE SHIPS CENTER OF

GRAVITY

WL

GD= DL+DC+DS

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SHIPS STABILITY

METACENTER MOMENT=UPSERTING MOMENT

M = D h sin O

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RIGHTING MOMENT

THE TENDENY OF A FORCE TO

A PIVOT POINT

C0

G

m

C1

M = D h sinQ

DVg

h

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GRAVITY

The force of gravity acts vertically downward throught

the ships center of gravity.

D=Vg

W L

Vg

D

C

G

Application of following terms to

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pp g

overall stability

(a)Couple

(b)Righting arm (GZ)

(c)Righting moment (RM) - RM= GZ (W)

(d)Upsertting moment

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DEFINITIONS

Couple. Since the forces of buoyancy and gravity are equal and act

along parallel lines, but in opposite directions, a rotation is developed

Righting arm.The distance between the forces of buoyancy and

gravity is know as the ships righting arm.

Righting moment. The righting moment is equal to the ships

Righting arm multiplied by the ships displacement.

Metacentric height. The distance between center of gravity G and

Metacener M .

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The development of the static stability curve from the

cross

curves of stability

Foctors involed:

G does not change position as heeling angle

changes

- C is always at the geometric center of the volume

of the underwater hull

- the shape of the underwater hull changes as

heeling angle changes

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Using curves,find

(a) Maximum rigting

arm (GZ) GZ=h(b) Angle of heel where

maximum GZ arm ocurs

l staticmaximum(c) Range of critical

stability Qcritical

SHIPS STABILITY CURVE

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SHIPS STABILITY

STABILITY CURVES ELEMENTS

lst

Qh

57.3

l static max

Q critical

STATIC STABILITY CURVE

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When a ship is inclined through all angles of

heel,and the

righting arm for each angle is measured, the

statical stabilitycurve is produced. This

curve is asnapshotof the ships stability at

information can beobtained from this curve,

including:

1. Range of Stability:

This ship will generate Righting

Arms when inclined from 0 deg. Till to approximately 74 dg.

2. Maximum Righting Arm:The angle of inclination

where the maximum Righting Arm occurs

3. Danger Angle:Onehalf the angle of the maximum

Righting Arms.

DRAFT DIAGRAM AND FUNCTIONS

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DRAFT DIAGRAM AND FUNCTIONS

OF FORM

The Draft Diagram is a nomogram located in

Section II(a) of the Damage Control Book.

It is used for determining the ships displacement, as well as other

properties of the ship, including:

- Moment to Trim One Inch (MT1);- Tons per Inch Immersion (TPI);

- Height of Metacenter (KM);

- Longitudinal Center of Flotation (LCF)

- Longitudinal Center of Buoyancy(LCB)

-Displacement (D)-VOLUME V m

-Weight, drafting per 1 cm

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HYDROSTATIC CURVES

SHIPS FLOATING BODY FUNCTIONS CAN CALCULATING

BY HYDROSTATIC CURVES. THIS CURVES IS FUNCTIONS

FLOATING SHIPS BODY STABILITY AND UNDERSEA

SHIPS BODY CAPITICY.

ARGUMENT FOR CALCULATING IS SHIPS DRAFT

FUNCTIONS FOR CALCULATING:

a) DISPLACEMENT D

b) VOLUME V

c) FLOATING CENTER Xf

f) SQUERE OF WATERLINE S

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HYDROSTATIC CURVES

SHIPS FLOATING BODY FUNCTION CURVESDRAFT

FUNCTIONS

V

D

S

Xf

Zc r

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COUPLE

Q

m

C

G

C1

M=D h sin Q

l st

h

D

Vg

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PLIMSOL DISC

WNA

W

S

TF

TF

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LIST

Q

Q

W1

L1

WO Lo

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ROLLING PERIOD

SHIPS STABILITY AND ROLLING PERIOD

W L

T= C B

h

ROLLING PERIODTh lli i d f h hi d d d f hi bili Th f l

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The rolling period of the ships dependenced from ships stability. The formula

Between ship,s stability and rolling :

T = c*B/sqr GM

I n this formula:

T rolling period in sec.

c - constanta

B the ships beam to outside of hull.

Note: the constanta c dependenced from ships displacements.

There are the followings meanings:

c=0.88 when ship is empty or ballast;

c=0.78 - when the ship has on board amout 20 %

c=0.75 when liquids on board 10%

c=0.73 when all liquids on board amout 5%

HOWEVER, for all lagers ships Lloyds Register of shipping and the 1991 HMSO

Code of Practice for Ro-Ro ships use c= 0.7

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SHIPS STABILITY VARIATIONS

C0

G0

m0

h0

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SHIPS STABILITY VARIATIONS

C0

G0

m0

h0

p

C1G1

m1

h1

h0 < h1

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SHIPS STABILITY VARIATIONS

C0

G0

m0

h0

P1 P2

G1

m1

h1

h0 >h1

C1

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SHIPS STABILITY VARIATIONS

MOVING CARGO

C0

G0

m0

h0

STABILITY REFERENCES POINTS BEFORE MOVING

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SHIPS STABILITY VARIATIONS

MOVING CARGO

C0

G0

m0

h0

STABILITY REFERENCES POINTS BEFORE MOVING DOWN

P1

P2

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SHIPS STABILITY VARIATIONS

MOVING CARGO

C0

G0

m0

h0

STABILITY REFERENCES POINTS AFTER MOVING DOWN

P1 P2

G1

h1

h1 > h0

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SHIPS STABILITY VARIATIONS

MOVING CARGO

C0

G0

m0

h0

STABILITY REFERENCES POINTS BEFORE MOVING UPWARD

P1 P2

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SHIPS STABILITY VARIATIONS

MOVING CARGO

C0

G0

m0

h0

STABILITY REFERENCES POINTS AFTER MOVING UPVARD

P1

P2

G1h1

h0 > h1

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SHIPS STABILITY VARIATIONS

G0

C0

W0L0G1

m

h0

h1

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SHIPS STABILITY VARIATIONS

FREE LIQUID AREA

P0

W0L0

C0

G0

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SHIPS STABILITY VARIATIONS

FREE LIQUID AREA

Q1 P1

P2

M1

M2

Y1

Y2

M2>M1 Q2>

Q1

Mcargo

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SHIPS STABILITY VARIATIONS

HANGING CARGO Q

lz

P

Mcargo= Pcargo lz sin Q

W0

L0

W1

L1

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TRIM

Trim means different between draft fore TF and draft aft TAF

TF

TAF

W L

W1

L1

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SHIPS TRIM DIAGRAM

Tf

TAf

m

m

12 3 4 5 6 7 8 9

2

3

4

5

6

7

8

9

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SHIPS TRIM DIAGRAMDt

Xc m0-1 0-2-3-4-5 1 2

3

200

600

400

800

200

600

4000

SHIPS STABILITY VARIATIONS

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TRIM

Trim means different between draft fore TF and draft aft TAF

TF

TAF

W L

W1

L1P

SHIPS TRIM BEFORE SHIFTING CARGO

lx

Mdif

D H

SHIPS STABILITY VARIATIONS

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TRIM

Trim means different between draft fore TF and draft aft TAF

TF0

TAF0

W L

W1

L1P

TF1

AF1

SHIPS TRIM AFTER SHIFTING CARGO

Plx

d =P lx

D HL

L

d

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LIST

Q

Q

W1

L1

WOLo

SHIPS STABILITY VARIATIONS

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LIST

WOLo

P

SHIPS LIST BEFORE SHIFTING CARGO

SHIPS STABILITY VARIATIONS

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LIST

WO Lo

P Ply

W1

L1

Q

tg Q = P ly

D h