2SHIP’S STABILITYSHIP’S STABILITY IS THE TENDENCY OF SHIP TO ROTARE ONE WAY OR THE OTHER WHEN FORCIBLY INCLINED
3WHAY IS STABILITY IS SO IMPORTENT ? IF THE SHIP LOST STABILITY WHAT WILL BE HAPPENED:1. LOST OF MOBILE2. LOST THE HUMANS LIFES 3. LOST THE SHIP4. LOST THE CARGO5. OIL POLLUTION
4FUNDAMENTALS OF STABILITY STABILITY is the tendency of vessel to rotate one way or theother when forcibly inclined.IMPORTENT !!Ship’s stability can’t catch directlyStability can define only by calculating
5HOW 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 forms4.By special cargo plan computer5.By standard PC with special cargo plan program6.By special or standard hand calculator
6SHIP’S STABILITY CRITERIAS THERE ARE TWO SHIP’S STABILITY CRITERIAS:1 h>0 ship’s metacenter height always positive.2 Zg < Zcriticalh = Zm – ZgZg defined by calculatingZm define according hydrostatic curvesZg critical define according special diagram.
7SHIP’S STABILITY CALCULATING SHIP’S STABILITY CALCULATING BY MOMENT FORMULAS.MAIN OBJECT OF CALCULATING TO DEFINE SHIP’S STABILITY CRITERIAS:GM=h METACENTER HEIGHTZg SHIP’S GRAVITY HEIGHTMOMENT FORMULA:D0Z0+P1Z1+P2Z2+…….+PnZnZg =D0 + P1 +P2 + …….. + Pn
11STABILITYINITIAL 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.
12INITIAL SHIP’S STABILITY Initial ship’s stability when ship inclinating from 7 till12 degrees. Ship’s underwater body did not change volumeV0=V1V1mL1V0GwLC1W1C
13INITIAL METACENTRIC FORMULA M=D lstQstmlst=hsinQhM=D h sin QlstGDVgC1C
14SHIP’S STABILITY CALCULATING Initial stability calculating by ship’s stability triangleCalculating formula lst= h sinQOverall stability calculating by hydrostatic ship’s body formula lfDynamic stability is the area under the static stability curveDynamic stability also potential energy available to return the ship to the upringing
16SHIP’S BADY FORM STABILITY ARMS lf PHANTACORENSSHIP’S BADY FORM STABILITY ARMS lflf2.880902.470601.650ARMS lf401.2300.8200.410400060008000100001200016000200001400018000DISPLACEMENT
17METACENTRIC HEIGHTMetacentric height GM is calculated by subtracting KGFrom KM (GM=KM-KG), GM is a measure of the ship.sstability. KM=h.With initial stability(0 – 10 deg.) the metacenter does notmove, 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 ship’s MetacentricHeight, GM.IMPORTENT !Thus , GM is a good measure of the ship’sinitial stability.
32STABILITY CONDITIONSThe positions of Gravity and the Metacenter will indicate the initial stabilityof a ship.Following damage, the ship will assume one of the following three stabilityconditions:1. POSITIVE STABILITY. The metacenter is located abovethe ship’s center of gravity.As the ship is inclined, Righting Arm are created which tendto return the ship to it’s original, vertical position.2. NEUTRAL STABILITY. The metacenter and the ship’scenter 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 isabove the metacenter.As the ship is inclined, negative Righting Arms (called upsettingarms) are created which tend to capsize the ship.
33METACENTRIC FORMULA OVERALL h=Zm - ZG M M=( lf —lst)D m h lst G D C1 W0L0VgDC1ZmZGlfW1CM- UPSERTING MOMENT
34METACENTRIC HIGHT h 57,3 Mst lst Q METACENTRIC HIGHT IS FIRST DERIVATIVE SHIP”S STABILITY CURVEMstlsthQ57,3
35METACENTER MOMENT IS UPSERTING MOMENT METACENTER HEIGHTMetacenter height GM is a determine of ship’s stability curveL1mhLWGC1W1CMETACENTER MOMENT IS UPSERTING MOMENTM= D h sin Q
41DYNAMIC STABILITYThe dynamic stability is the area under the curve in metre-radiansMultiplated by the ship,s displacement in tonnes. It is areas underthe GZCurve which are required for checking stability criteria whichdependingUpon the ship,s data may be expressed in metre-degrees ormetre-radians.The area unde GZ curve also the potential energy available toreturn theShip to the upringht.Principle of conservation of energy, the potential energyin converted intoRotation energy as the ship moves towards the upright.
43STABILITY ELEMENTSTHE LAW OF BUOYANCYTHE LAW OF GRAVITYSTABILITY REFERENCE POINTSLINEAR MESURMENTS IN STABILITYTHE STABILITY TRIANGLERIGHTING MOMENTSTATIC STABILITY CURVE DYNAMIC STABILITY CURVE ROLLING PERIOD
44Learning ObjectivesComprehend the concepts of hydrostatics, buoyancy, and Archimedes' principleComprehend static equilibrium of a floating vessel and the relationship of the centers of gravity and buoyancy to righting arms and stabilityComprehend and identify positive, negative and neutral conditions of stabilityComprehend the effects of movements of the centers of gravity and buoyancy on vessel stabilityKnow how ship's stability curves are derived and comprehend their use in determining stability condition
45DefinitionsDraftFreeboardDepth of hullReserve buoyancyList / Trim
46SHIP’S HULL MARKINGSAt XVIII hundred one Englishman calledPLIMSOL in Great Britan Parlament fildsfor marcks on the hull to for Safe shipping.Now thats marks called PLIMSOL MARKS.
47PLIMSOL DISC PLIMSOL DISC DIVAIDING SHIP”S BODY IN TWO PARTS: 1. RESERVE BUOYANCY2. DISPLACEMENTRESERVE BOYANCYWLDISPLACEMENT
48FREE BOARD SHIP’S MAIN FREE BOARD MEENS SHIP’S RESERVE BUOYANCY DRAFT SHIP’S MAIN DRAFT MEENS SHIP’S DISPLACEMENT
49RESERVE BUOYANCYMAINTAIN FREEBOARD – RASERVE BUOYANCY PRIOR TO PREVENT LIMITING DRAFTS ARE ASSIGNED TO EXCESIVE HULL STRESS AS A RESULT OF OVERLOADING
52Buoyancy Archimedes' principle Calculations of displacement (W) The effect of salt water and fresh water on displacement (relate to draft)[1/35 vs 1/36]
53Archimede’s principle BOYADA body immersed (or floating) in water willbuoyedARCHIMEDE’S FORCEBy a force equal to the weight of the waterdisplaced.
54THE LAWS OF BUOYANCYFloatating objects posses the property of buoyancy.A floatating body displaces a volume of water equal ina body immersed (or floating) in water will be duoyedup by a force equal to the weight of the water displacedD=VgDLWGCVg
56PLIMSOL MARKS (Load lines) Markings of minimum allowable freeboard for registred cargo-Carryng ships.Located amidships on both the port and starboardsides the ship.Since the required minimum freeboard varies with water densityand 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 AtlanticTFFTSWWNA
57SHIP’S HULL MARKINGS Calculative Draft Marks Used for determining displacement and other propertiesof 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 height2. Arabic numerals in height
60SHIP’S HULL MARKINGSNavigational Draft MarksShip’s operational drafts.These draft marks include the depth of any projections below the keel of the ship.Limiting Draft MarksLimiting drafts are assigned to maintain reserve buoyancy (freeboard) prior to damage, and to prevent excessive hull stresses as a result of overloading.
61DISPLACEMENT GRAVITY MOMENT The weight of the volume of water that is displaced by theunderwater portion of the hull is equal to theweight of the shipsGRAVITYThe force of gravity acts vertically downward through the ship’s centerOf gravity. The magnitude of the force depends on the ship’s 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.
63GRAVITYTHE FORCE OF GRAVITY ACTS VERTICALY DOWNWARD THROUGHT THE SHIP”S CENTER OF GRAVITYWGLDL+DC+DSD=
64SHIP’S STABILITYMETACENTER MOMENT =UPSERTING MOMENTM = D h sin O
65RIGHTING MOMENTTHE TENDENY OF A FORCE TO PRODUCE A ROTATION ABOUT A PIVOT POINTmM = D h sinQhVgGDC1C0
66GRAVITYThe force of gravity acts vertically downward throught the ship’s center of gravity.D=VgDLWGCVg
67Application of following terms to overall stability Couple(b)Righting arm (GZ)(c)Righting moment (RM) - RM= GZ (W)(d)Upsertting moment
68DEFINITIONSCouple. Since the forces of buoyancy and gravity are equal and actalong parallel lines, but in opposite directions, a rotation is developed.Righting arm. The distance between the forces of buoyancy andgravity is know as the ship’s righting arm.Righting moment. The righting moment is equal to the ship’sRighting arm multiplied by the ship’s displacement.Metacentric height. The distance between center of gravity G andMetacener M .
69- G does not change position as heeling angle The development of the static stability curve from the cross curves of stabilityFoctors involed:- G does not change position as heeling anglechanges- C is always at the geometric center of the volumeof the underwater hull- the shape of the underwater hull changes asheeling angle changes
70SHIP’S STABILITY CURVE Using curves,find(a) Maximum rigting arm (GZ) GZ=h(b) Angle of heel where maximum GZ arm ocursl static maximum(c) Range of critical stability Q criticalSHIP’S STABILITY CURVE
71SHIP’S STABILITY STABILITY CURVES ELEMENTS h Q Q critical lst l static maxhQ57.3Q critical
72STATIC STABILITY CURVE When a ship is inclined through all angles of heel,and therighting 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 occursDanger Angle:One half the angle of the maximum Righting Arms.
73DRAFT DIAGRAM AND FUNCTIONS OF FORM The Draft Diagram is a nomogram located inSection II(a) of the Damage Control Book.It is used for determining the ship’s displacement, as well as otherproperties 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
74DRAFT NOMOGRAM Tm Dt Vm M t/cm P t/cm 8.2 18000 17900 19900 26.5 7.8 170001686018800267.216000158451760025.56.8150001484016600256.414000138401550024.56.01300012820245.612000118201460023.55.2110001082014400234.81000098201420022.54.49000882022TmDtVm3M t/cmP t/cm
75HYDROSTATIC CURVESSHIP’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 DRAFTFUNCTIONS FOR CALCULATING:a) DISPLACEMENT Db) VOLUME Vc) FLOATING CENTER Xfd) BOYAD CENTER XC Zce METACENTER RADIUS rf) SQUERE OF WATERLINE S
76HYDROSTATIC CURVES SHIP’S FLOATING BODY FUNCTION CURVES V Zc r Xf D S DRAFTVZcrXfDSFUNCTIONS
80ROLLING PERIODC BT=SHIP”S STABILITY AND ROLLING PERIODhLW
81B – the ship’s beam to outside of hull. ROLLING PERIODThe rolling period of the ship’s dependenced from ship’s stability. The formulaBetween ship,s stability and rolling :T = c*B/sqr GMIn this formula:T – rollinperiod in sec.c - constantaB – 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 HMSOCode of Practice for Ro-Ro ships use c= 0.7
82SHIP’S STABILITY VARIATIONS LOADING CARGOm0h0G0C0STABILITY REFERENCES POINTS BEFORE LOADING
83SHIP’S STABILITY VARIATIONS h0 < h1LOADING CARGO IN HOLDm1m0h1h0G0G1C1C0pSTABILITY REFERENCES POINTS AFTER LOADING
84SHIP’S STABILITY VARIATIONS h0 >h1LOADING CARGO AT DECKm1P2P1m0h1h0G1G0C1C0STABILITY REFERENCES POINTS AFTER LOADING
85SHIP’S STABILITY VARIATIONS MOVING CARGOm0h0G0C0STABILITY REFERENCES POINTS BEFORE MOVING
86SHIP’S STABILITY VARIATIONS MOVING CARGOP2m0P1h0G0C0STABILITY REFERENCES POINTS BEFORE MOVING DOWN
87SHIP’S STABILITY VARIATIONS h1 > h0MOVING CARGOm0h0h1G0G1C0P2P1STABILITY REFERENCES POINTS AFTER MOVING DOWN
88SHIP’S STABILITY VARIATIONS MOVING CARGOm0h0G0C0P2P1STABILITY REFERENCES POINTS BEFORE MOVING UPWARD
97SHIP’S TRIM DIAGRAM Dt 4000 Tf=6m TAf=6.4m 3600 5.8m 6.0m 5.4m 3200 28005.2m4.8m4.6m24004.4m4.4m16003.8m3.2m4.0m3.0m12003.2m3.6m3-5-4-3-2-112Xc m
98TRIM W1 lx TAF L1 P TF SHIP’S TRIM BEFORE SHIFTING CARGO SHIP’S STABILITY VARIATIONSTRIMTrim means different between draft fore TF and draft aft TAFW1WLlxNOTE Ship”s trim is one element of ship”s stability and buoyancyTAFL1PTFSHIP’S TRIM BEFORE SHIFTING CARGOMdifD H
99TRIM W1 TAF0 P P L1 TAF1 TF0 TF1 L SHIP’S TRIM AFTER SHIFTING CARGO SHIP’S STABILITY VARIATIONSTRIMTrim means different between draft fore TF and draft aft TAFP lxd =LD HW1WLNOTE Ship”s trim is one element of ship”s stability and buoyancyTAF0PPL1TAF1dlxTF0TF1LSHIP’S TRIM AFTER SHIFTING CARGO