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**Principles of Ship’s Stability**

PETRAS PIKSRYS

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SHIP’S STABILITY SHIP’S STABILITY IS THE TENDENCY OF SHIP 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**

STABILITY is the tendency of vessel to rotate one way or the other when forcibly inclined. IMPORTENT !! Ship’s stability can’t catch directly Stability can define only by calculating

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**HOW CALCULATING SHIP”S STABILITY AND CARCO PLAN ?**

1.By previous similar cargo plan. 2.By standard cargo plan according “STABILITY 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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**SHIP’S STABILITY CRITERIAS**

THERE ARE TWO SHIP’S STABILITY CRITERIAS: 1 h>0 ship’s metacenter height always positive. 2 Zg < Zcritical h = Zm – Zg Zg defined by calculating Zm define according hydrostatic curves Zg critical define according special diagram.

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**SHIP’S STABILITY CALCULATING**

SHIP’S STABILITY CALCULATING BY MOMENT FORMULAS. MAIN OBJECT OF CALCULATING TO DEFINE SHIP’S STABILITY CRITERIAS: GM=h METACENTER HEIGHT Zg SHIP’S GRAVITY HEIGHT MOMENT FORMULA: D0Z0+P1Z1+P2Z2+…….+PnZn Zg = D0 + P1 +P2 + …….. + Pn

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**SHIP’S STABILITY CALCULATING**

Zg critical CURVE 6.60 6.50 6.40 Zg critical 6.30 6.20 6.10 8000 10000 12000 14000 16000 18000 20000 D

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**WHO CALCULATING SHIP’S CARGO PLAN AND STABILITY?**

1.CARGO OFFICER (ch.mate) 2.PORT CARGO OFFICER (supercargo) 3.SHIP’S MASTER

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SHIP’S STABILITY

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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 given condition of loading. DYNAMIC STABILITY - The work done in heeling a ship to a given angle of heel.

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**INITIAL SHIP’S STABILITY**

Initial ship’s stability when ship inclinating from 7 till12 degrees. Ship’s underwater body did not change volume V0=V1 V1 m L1 V0 G w L C1 W1 C

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**INITIAL METACENTRIC FORMULA**

M=D lst Qst m lst=hsinQ h M=D h sin Q lst G D Vg C1 C

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**SHIP’S STABILITY CALCULATING**

Initial stability calculating by ship’s stability triangle Calculating formula lst= h sinQ Overall stability calculating by hydrostatic ship’s body formula lf Dynamic stability is the area under the static stability curve Dynamic stability also potential energy available to return the ship to the upringing

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STABILITY TRIANGLE m lst =hsin Q h Q l f l st G Vg D C1 lf C

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**SHIP’S BADY FORM STABILITY ARMS lf**

PHANTACORENS SHIP’S BADY FORM STABILITY ARMS lf lf 2.8 80 90 2.4 70 60 1.6 50 ARMS lf 40 1.2 30 0.8 20 0.4 10 4000 6000 8000 10000 12000 16000 20000 14000 18000 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.s stability. 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, is directly prportional to the size of the ship’s Metacentric Height, GM. IMPORTENT ! Thus , GM is a good measure of the ship’s initial stability.

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METACENTRIC HEIGHT m h L W G a a C

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**MAIN STABILITY POINTS There are three main stability points:**

m- metacenter is the end of hydrostatic force when ship listing. G- centre of ship gravity C- centre of ship underwater body.

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SHIP’S STABILITY STABILITY REFERENCE POINTS m h Zm G WO r Lo ZG a C Zc

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**MAIN STABILITY POINTS h Wo m Q LO a G C m metacenter**

G center of gravity C center of buoyancy m Q L1 h Q Wo LO a G W1 C C1

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SHIP’S STABILITY METACENTER m C0

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**SHIP’S STABILITY METACENTRIC HEIGHT FORMULAS h=r-a h=zm – zG**

h=zc - ro - zG

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METACENTRIC HEIGHT METACENTRIC HEIGHT MEENS SHIP’S INITIAL STABILITY m h L W G r0 a C

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**Three states of static equilibrium**

(a) Positive stability - m above G (b) Neutral stability – m and G in the same position ( c )Negative stability –m below G m G G m h=O h<O h>O G m c b a

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**POSITIVE SHIP’S STABILITY**

Positive ship’s stability when m above G h>0 m L1 h W L G W1 C1 C

27
**SHIP’S STABILITY CURVE**

POSITIVE SHIP’S STABILITY L l st h>0 h 57, 3 Q Q

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**NEUTRAL SHIP’S STABILITY**

Neutral ship’s stability when m and G in the same position h=0 G m L W C C1

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SHIP’S STABILITY NEUTRAL SHIP’S STABILITY h=0 lst Q

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**NEGATIVE SHIP’S STABILITY**

Negative ship’s stability when m below G h<0 L1 G h W L m C1 W1 C

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**NEGATIVE SHIP’S STABILITY**

Mst Qst 57.3 -h

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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 ship’s center of gravity. As the ship is inclined, Righting Arm are created which tend to return the ship to it’s original, vertical position. 2. NEUTRAL STABILITY. The metacenter and the ship’s 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 OVERALL h=Zm - ZG M M=( lf —lst)D m h lst G D C1**

W0 L0 Vg D C1 Zm ZG lf W1 C M- UPSERTING MOMENT

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**METACENTRIC HIGHT h 57,3 Mst lst Q**

METACENTRIC HIGHT IS FIRST DERIVATIVE SHIP”S STABILITY CURVE Mst lst h Q 57,3

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**METACENTER MOMENT IS UPSERTING MOMENT**

METACENTER HEIGHT Metacenter height GM is a determine of ship’s stability curve L1 m h L W G C1 W1 C METACENTER MOMENT IS UPSERTING MOMENT M= D h sin Q

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DYNAMIC STABILITY W L

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**SHIP’S DYNAMIC STABILITY**

DYMAMIC MOMENT M M DYNAMIC MOMENT Q

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SHIP’S STABILITY STATIC MOMENT CURVE M Q

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**SHIP’S DYNAMIC STABILITY**

MAXIMUM DYNAMIC ANGLE Qdyn WHEN S1= S2 M S2 S1 Q Q static Q dyn Q dyn max

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**SHIP’S DYNAMIC CURVE S=Mdyn Mdyn**

SHIP’S DYNAMIC STABILITY CURVES APPLICATES IS EQUVALENT STATIC CURVES AREA S=Mdyn Mdyn S Mdyn Q

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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 under the GZ Curve which are required for checking stability criteria which depending Upon the ship,s data may be expressed in metre-degrees or metre-radians. 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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DYNAMIC STABILITY CURVE Mst Mst Mdin Md Q Q max

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STABILITY ELEMENTS THE LAW OF BUOYANCY THE LAW OF GRAVITY STABILITY 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 buoyancy to righting arms and stability Comprehend and identify positive, negative and neutral conditions of stability Comprehend the effects of movements of the centers of gravity 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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Definitions Draft Freeboard Depth of hull Reserve buoyancy List / Trim

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SHIP’S HULL MARKINGS At 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 SHIP”S BODY IN TWO PARTS:**

1. RESERVE BUOYANCY 2. DISPLACEMENT RESERVE BOYANCY W L DISPLACEMENT

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**FREE BOARD SHIP’S MAIN FREE BOARD MEENS SHIP’S RESERVE BUOYANCY DRAFT**

SHIP’S MAIN DRAFT MEENS SHIP’S DISPLACEMENT

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RESERVE BUOYANCY MAINTAIN FREEBOARD – RASERVE BUOYANCY PRIOR TO PREVENT LIMITING DRAFTS ARE ASSIGNED TO EXCESIVE HULL STRESS AS A RESULT OF OVERLOADING

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**FREE BOARD MEENS RESERVE BUOYANCY**

TF FREE BOARD F S WL W WNA

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DRAFT MAIN DRAFT MEENS SHIP”S DISPLACEMENT W L DRAFT

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**Buoyancy Archimedes' principle Calculations of displacement (W)**

The effect of salt water and fresh water on displacement (relate to draft) [1/35 vs 1/36]

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**Archimede’s principle**

BOYAD A body immersed (or floating) in water will buoyed ARCHIMEDE’S FORCE By a force equal to the weight of the water displaced.

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THE LAWS OF BUOYANCY Floatating objects posses the property of buoyancy. 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 D=Vg D L W G C Vg

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SHIP’S BUOYANCY D=V*g L G W D V*g C ARCHIMEDES FORCE

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**PLIMSOL MARKS (Load lines) **

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 TF F T S W WNA

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**SHIP’S 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 = m XVII XVI XV XIV XIII

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DRAFT IN METRES 1 ft = m 44 42 40 38 36

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SHIP’S HULL MARKINGS Navigational Draft Marks Ship’s operational drafts. 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 damage, and to prevent excessive hull stresses as a result of overloading.

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**DISPLACEMENT GRAVITY MOMENT**

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 GRAVITY The force of gravity acts vertically downward through the ship’s center Of gravity. The magnitude of the force depends on the ship’s total weight. MOMENT The 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 DLS – Weight light ship DS - Weight supply DC - Weight cargo

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GRAVITY THE FORCE OF GRAVITY ACTS VERTICALY DOWNWARD THROUGHT THE SHIP”S CENTER OF GRAVITY W G L DL+DC+DS D=

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SHIP’S STABILITY METACENTER MOMENT =UPSERTING MOMENT M = D h sin O

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RIGHTING MOMENT THE TENDENY OF A FORCE TO PRODUCE A ROTATION ABOUT A PIVOT POINT m M = D h sinQ h Vg G D C1 C0

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GRAVITY The force of gravity acts vertically downward throught the ship’s center of gravity. D=Vg D L W G C Vg

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**Application of following terms to overall stability**

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 ship’s righting arm. Righting moment. The righting moment is equal to the ship’s Righting arm multiplied by the ship’s displacement. Metacentric height. The distance between center of gravity G and Metacener M .

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**- G does not change position as heeling angle**

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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**SHIP’S STABILITY CURVE**

Using curves,find (a) Maximum rigting arm (GZ) GZ=h (b) Angle of heel where maximum GZ arm ocurs l static maximum (c) Range of critical stability Q critical SHIP’S STABILITY CURVE

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**SHIP’S STABILITY STABILITY CURVES ELEMENTS h Q Q critical lst**

l static max h Q 57.3 Q critical

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**STATIC STABILITY CURVE**

When a ship is inclined through all angles of heel,and the righting arm for each angle is measured, the statical stability curve is produced. This curve is a “snapshot”of the ship’s stability at that particular loading condition.Much information can be obtained from this curve, including: Range of Stability: This ship will generate Righting Arms when inclined from 0 deg. Till to approximately 74 dg. Maximum Righting Arm: The angle of inclination where the maximum Righting Arm occurs Danger Angle:One half the angle of the maximum Righting Arms.

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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 ship’s 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 -Moment, diferenting per 1 cm -Weight, drafting per 1 cm

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**DRAFT NOMOGRAM Tm Dt Vm M t/cm P t/cm 8.2 18000 17900 19900 26.5 7.8**

17000 16860 18800 26 7.2 16000 15845 17600 25.5 6.8 15000 14840 16600 25 6.4 14000 13840 15500 24.5 6.0 13000 12820 24 5.6 12000 11820 14600 23.5 5.2 11000 10820 14400 23 4.8 10000 9820 14200 22.5 4.4 9000 8820 22 Tm Dt Vm 3 M t/cm P t/cm

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HYDROSTATIC CURVES SHIP’S FLOATING BODY FUNCTIONS CAN CALCULATING BY HYDROSTATIC CURVES. THIS CURVES IS FUNCTIONS FLOATING SHIP’S BODY STABILITY AND UNDERSEA SHIP’S BODY CAPITICY. ARGUMENT FOR CALCULATING IS SHIP’S DRAFT FUNCTIONS FOR CALCULATING: a) DISPLACEMENT D b) VOLUME V c) FLOATING CENTER Xf d) BOYAD CENTER XC Zc e METACENTER RADIUS r f) SQUERE OF WATERLINE S

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**HYDROSTATIC CURVES SHIP’S FLOATING BODY FUNCTION CURVES V Zc r Xf D S**

DRAFT V Zc r Xf D S FUNCTIONS

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COUPLE m M=D h sin Q h Q l st G Vg D C1 C

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PLIMSOL DISC TF T F S W WNA

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LIST Q L1 Lo Q WO W1

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ROLLING PERIOD C B T= SHIP”S STABILITY AND ROLLING PERIOD h L W

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**B – the ship’s beam to outside of hull. **

ROLLING PERIOD The rolling period of the ship’s dependenced from ship’s stability. The formula Between ship,s stability and rolling : T = c*B/sqr GM In this formula: T – rollinperiod in sec. c - constanta B – the ship’s beam to outside of hull. Note: the constanta c dependenced from ship’s displacements. There are the followings meanings: c=0.88 – when ship is empty or ballast; c= 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 Lloyd’s Register of shipping and the 1991 HMSO Code of Practice for Ro-Ro ships use c= 0.7

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**SHIP’S STABILITY VARIATIONS**

LOADING CARGO m0 h0 G0 C0 STABILITY REFERENCES POINTS BEFORE LOADING

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**SHIP’S STABILITY VARIATIONS**

h0 < h1 LOADING CARGO IN HOLD m1 m0 h1 h0 G0 G1 C1 C0 p STABILITY REFERENCES POINTS AFTER LOADING

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**SHIP’S STABILITY VARIATIONS**

h0 >h1 LOADING CARGO AT DECK m1 P2 P1 m0 h1 h0 G1 G0 C1 C0 STABILITY REFERENCES POINTS AFTER LOADING

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**SHIP’S STABILITY VARIATIONS**

MOVING CARGO m0 h0 G0 C0 STABILITY REFERENCES POINTS BEFORE MOVING

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**SHIP’S STABILITY VARIATIONS**

MOVING CARGO P2 m0 P1 h0 G0 C0 STABILITY REFERENCES POINTS BEFORE MOVING DOWN

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**SHIP’S STABILITY VARIATIONS**

h1 > h0 MOVING CARGO m0 h0 h1 G0 G1 C0 P2 P1 STABILITY REFERENCES POINTS AFTER MOVING DOWN

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**SHIP’S STABILITY VARIATIONS**

MOVING CARGO m0 h0 G0 C0 P2 P1 STABILITY REFERENCES POINTS BEFORE MOVING UPWARD

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**SHIP’S STABILITY VARIATIONS**

h0 > h1 MOVING CARGO P2 m0 P1 h1 h0 G1 G0 C0 STABILITY REFERENCES POINTS AFTER MOVING UPVARD

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**SHIP’S STABILITY VARIATIONS**

LOADING CARGO m h0 h1 G0 G1 L0 W0 C0

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**SHIP’S STABILITY VARIATIONS**

FREE LIQUID AREA G0 L0 W0 C0 P0

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**SHIP’S STABILITY VARIATIONS**

M Moment liquid SHIP’S STABILITY VARIATIONS M Moment upserting FREE LIQUID AREA m L1 G0 Q L0 W0 C1 C0 W1 P1 P1

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**SHIP’S STABILITY VARIATIONS**

M1 FREE LIQUID AREA Y1 Q1 M2 P1 Y2 P2 Q2>Q1 M2>M1 Q2

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**SHIP’S STABILITY VARIATIONS**

Mcargo SHIP’S STABILITY VARIATIONS HANGING CARGO Q lz W0 L1 P L0 W1 Mcargo= Pcargo lz sin Q

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TRIM Trim means different between draft fore TF and draft aft TAF W1 W L NOTE Ship”s trim is one element of ship”s stability and buoyancy TAF L1 TF

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**SHIP’S TRIM DIAGRAM TAf Tf m 9 8 D=19000t 7 6 5 4 3 2 1 2 3 4 5 6 7 8**

Xc=28m 7 18000t 30m 6 32m 16000t 17000t 34m 15000t 5 36m 14000t 38m 4 40m 10000t 42m 3 9000t 44m 8000t 7000t 46m 2 48m Tf 1 2 3 4 5 6 7 8 9 m

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**SHIP’S TRIM DIAGRAM Dt 4000 Tf=6m TAf=6.4m 3600 5.8m 6.0m 5.4m 3200**

2800 5.2m 4.8m 4.6m 2400 4.4m 4.4m 1600 3.8m 3.2m 4.0m 3.0m 1200 3.2m 3.6m 3 -5 -4 -3 -2 -1 1 2 Xc m

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**TRIM W1 lx TAF L1 P TF SHIP’S TRIM BEFORE SHIFTING CARGO**

SHIP’S STABILITY VARIATIONS TRIM Trim means different between draft fore TF and draft aft TAF W1 W L lx NOTE Ship”s trim is one element of ship”s stability and buoyancy TAF L1 P TF SHIP’S TRIM BEFORE SHIFTING CARGO Mdif D H

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**TRIM W1 TAF0 P P L1 TAF1 TF0 TF1 L SHIP’S TRIM AFTER SHIFTING CARGO**

SHIP’S STABILITY VARIATIONS TRIM Trim means different between draft fore TF and draft aft TAF P lx d = L D H W1 W L NOTE Ship”s trim is one element of ship”s stability and buoyancy TAF0 P P L1 TAF1 d lx TF0 TF1 L SHIP’S TRIM AFTER SHIFTING CARGO

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LIST Q L1 Lo Q WO W1

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**LIST Lo WO P SHIP’S STABILITY VARIATIONS**

SHIP’S LIST BEFORE SHIFTING CARGO

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**LIST WO Lo SHIP’S STABILITY VARIATIONS ly P P L1 Q W1 P ly tg Q = D h**

SHIP’S LIST AFTER SHIFTING CARGO

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