#### Transcript Ship`s Stability

# Principles of Ship’s Stability

**PETRAS PIKSRYS **

**SHIP’S STABILITY •SHIP’S STABILITY IS THE TENDENCY OF SHIP TO ROTARE ONE WAY OR THE OTHER WHEN FORCIBLY INCLINED**

**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**

**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**

**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**

**SHIP’S STABILITY CRITERIAS**

**• • • • THERE ARE TWO SHIP’S STABILITY CRITERIAS: • 1 h>0 ship’s metacenter height always positive.**

**• 2 Z g < Z critical h = Z m – Z g Z g defined by calculating Z m define according hydrostatic curves • Z g critical define according special diagram.**

**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 • Z g SHIP’S GRAVITY HEIGHT • MOMENT FORMULA: • • Z g • = D 0 Z 0 +P 1 Z 1 +P 2 Z 2+…….+ P n Z n D 0 + P 1 + P 2 + …….. + P n**

**SHIP’S STABILITY CALCULATING • Z g critical CURVE 6.60**

**6.50**

**6.40**

**Z g critical 6.30**

**6.20**

**6.10**

**8000 10000 12000 14000 16000 18000 20000**

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

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

**SHIP’S STABILITY**

**STABILITY INITIAL OVERALL DYNAMIC**

**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.**

**INITIAL SHIP’S STABILITY W w • Initial ship’s stability when ship inclinating from 7 till12 degrees. Ship’s underwater body did not change volume • V 0 =V 1 V 1 m L 1 V 0 G L 1 C 1 C**

**INITIAL METACENTRIC FORMULA**

**M=D l st l st =h sin Q M=D h sin Q m G l st D Q st V g h C 1 C**

**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 l the static stability curve • Dynamic stability also potential the upringing f • Dynamic stability is the area under energy available to return the ship to **

**STABILITY TRIANGLE**

**m l st =hsin Q l f h Q l st G Vg D l f C 1 C**

**PHANTACORENS SHIP’S BADY FORM STABILITY ARMS l f l f 2.8**

**2.4**

**1.6**

**1.2**

**0.8**

**0.4**

**80 70 60 50 40 30 20 10 90 4000 6000 8000 10000 12000 14000 16000 18000 20000 DISPLACEMENT**

**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.**

**W**

**METACENTRIC HEIGHT**

**m G h a a C L**

**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.**

**SHIP’S STABILITY**

**W O • STABILITY REFERENCE POINTS m Z m G r Z G Zc C h L o a**

**• • •**

**MAIN STABILITY POINTS**

**m metacenter G center of gravity C center of buoyancy m Q h L 1 W o W 1 a G C C 1 L O Q**

**SHIP’S STABILITY METACENTER m C 0**

**SHIP’S STABILITY • METACENTRIC HEIGHT FORMULAS • h=r-a • h=**

**z**

**m –**

**z**

**G • h=**

**z**

**c r o -**

**z**

**G**

**METACENTRIC HEIGHT**

**• METACENTRIC HEIGHT MEENS SHIP’S INITIAL STABILITY m W G h a r 0 C**

**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 a h>O m b G h=O G m c h**

**POSITIVE SHIP’S STABILITY**

**W 1 • Positive ship’s stability when m above G • h>0 h m L 1 W G L C C 1**

L

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

Q

**NEUTRAL SHIP’S STABILITY**

**• Neutral ship’s stability when m and G in the same position • h=0 W G m L C C 1**

**SHIP’S STABILITY**

**• NEUTRAL SHIP’S STABILITY l st h=0 Q**

**NEGATIVE SHIP’S STABILITY • Negative ship’s stability when m below G • h<0 W W 1 G m C h C 1 L 1 L**

**NEGATIVE SHIP’S STABILITY h=-0 M st 57.3**

**Q st**

**-h**

**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 ship’s center of gravity.**

**The metacenter is located above 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.**

**W 0 OVERALL**

**METACENTRIC FORMULA**

**• h=Z m Z G M m M=( l f —lst)D L 1 h G l st L 0 Vg l f C 1 Zm W 1 C Z G M- UPSERTING MOMENT**

**METACENTRIC HIGHT**

**METACENTRIC HIGHT IS FIRST DERIVATIVE SHIP”S STABILITY CURVE l st M st**

**h**

**Q**

57,3

**METACENTER HEIGHT**

**Metacenter height GM is a determine of ship’s stability curve • m L 1 W h G C 1 W 1 C METACENTER MOMENT IS UPSERTING MOMENT M= D h sin Q L**

**W DYNAMIC STABILITY L**

**M**

**SHIP’S DYNAMIC STABILITY**

**• DYMAMIC MOMENT M DYNAMIC MOMENT Q**

**SHIP’S STABILITY**

**• STATIC MOMENT CURVE M Q**

**SHIP’S DYNAMIC STABILITY**

**M • MAXIMUM DYNAMIC ANGLE Q dyn WHEN S 1 = S 2 S 2 S 1 Q static Q dyn Q dyn max Q**

**SHIP’S DYNAMIC CURVE**

**• SHIP’S DYNAMIC STABILITY CURVES APPLICATES IS EQUVALENT STATIC CURVES AREA S=M dyn M dyn M dyn Q**

**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.**

**M st DYNAMIC STABILITY CURVE M st M din M d Q max Q**

**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**

**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**

**Definitions**

**• Draft • Freeboard • Depth of hull • Reserve buoyancy • List / Trim**

**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.**

**W PLIMSOL DISC • PLIMSOL DISC DIVAIDING SHIP”S BODY IN TWO PARTS: • • 1. RESERVE BUOYANCY 2. DISPLACEMENT L RESERVE BOYANCY DISPLACEMENT**

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

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

**FREE BOARD**

**FREE BOARD MEENS RESERVE BUOYANCY FREE BOARD F TF WL S W WNA**

**DRAFT • MAIN DRAFT MEENS SHIP”S DISPLACEMENT W L DRAFT**

**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]**

**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.**

**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 D=Vg D W G C L V g**

**SHIP’S BUOYANCY**

**• D=V*g W G D C V*g L ARCHIMEDES FORCE**

**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**

**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**

**DRAFT IN FEETS • 1 ft = 0.3048 m XVII XVI XV XIV XIII**

**DRAFT IN METRES • 1 ft = 0.3048 m 44 42 40 38 36**

**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.**

**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 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. **

**DISPLACEMENT • D=D LS + D S + D C • D – Displacement • D LS – Weight light ship • D S - Weight supply • D C - Weight cargo**

**GRAVITY**

**• THE FORCE OF GRAVITY ACTS VERTICALY DOWNWARD THROUGHT THE SHIP”S CENTER OF GRAVITY W G D= D L+ D C+ D S L**

**SHIP’S STABILITY • METACENTER MOMENT =UPSERTING MOMENT**

**M = D h sin O**

**RIGHTING MOMENT**

**• THE TENDENY OF A FORCE TO PRODUCE A ROTATION ABOUT A PIVOT POINT h m G D M = D h Vg C 1**

sin

**Q C 0**

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

**Application of following terms to overall stability (a)Couple (b)Righting arm (GZ) (c)Righting moment (RM) - RM= GZ (W) (d)Upsertting moment**

**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 .

**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**

**SHIP’S STABILITY CURVE**

**Using **

**arm (GZ) GZ=h maximum GZ arm ocurs l curves,find (a) Maximum rigting (b) Angle of heel where **

**static maximum**

**(c) Range of critical stability Q**

**critical**

**h**

**SHIP’S STABILITY**

**• STABILITY CURVES ELEMENTS l st l static max 57.3**

**Q critical Q**

**STATIC STABILITY CURVE 1.**

**When a ship is inclined through all angles of curve is a**

“

**heel,and the righting arm for each angle is measured, the statical stability curve is produced. This 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

**2.**

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

**Maximum Righting Arm:**

The angle of inclination

**3.**

where the maximum Righting Arm occurs

**Danger Angle:One**

half the angle of the maximum Righting Arms.

**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 -Weight, drafting per 1 cm**

**8.2**

**7.8**

**7.2**

**6.8**

**6.4**

**6.0**

**5.6**

**5.2**

**4.8**

**4.4**

**T m**

**DRAFT NOMOGRAM**

**18000 17000 16000 15000 14000 13000 12000 11000 10000 9000 D t 17900 16860 15845 14840 13840 12820 11820 10820 9820 8820 V m 3 19900 18800 17600 16600 15500 15000 14600 14400 14200 14000 M t/cm 26.5**

**26 25.5**

**25 24.5**

**24 23.5**

**23 22.5**

**22 P t/cm**

**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 X f d) BOYAD CENTER X C Z c • e METACENTER RADIUS r f) SQUERE OF WATERLINE S**

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

**M=D h sin Q h**

**COUPLE**

**m Q l st G D Vg C 1 C**

**PLIMSOL DISC**

**TF F T S W WNA**

**W O W 1 LIST Q L 1 Q L o**

**ROLLING PERIOD**

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

**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=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 Lloyd’s Register of shipping and the 1991 HMSO Code of Practice for Ro-Ro ships use c= 0.7**

**SHIP’S STABILITY VARIATIONS • LOADING CARGO m 0 h 0 G 0 C 0 STABILITY REFERENCES POINTS BEFORE LOADING**

**SHIP’S STABILITY VARIATIONS h 0 < h 1 • LOADING CARGO IN HOLD m 0 m 1 h 1 h 0 G 0 G 1 C 1 C 0 p STABILITY REFERENCES POINTS AFTER LOADING**

**SHIP’S STABILITY VARIATIONS h 0 > h 1 • LOADING CARGO AT DECK 1 h 1 P 1 m 0 P 2 G 1 h 0 G 0 C 0 C 1 STABILITY REFERENCES POINTS AFTER LOADING**

**SHIP’S STABILITY VARIATIONS • MOVING CARGO m 0 h 0 G 0 C 0 STABILITY REFERENCES POINTS BEFORE MOVING**

**SHIP’S STABILITY VARIATIONS • MOVING CARGO P 1 m 0 P 2 h 0 G 0 C 0 STABILITY REFERENCES POINTS BEFORE MOVING DOWN**

**SHIP’S STABILITY VARIATIONS h 1 > h 0 • MOVING CARGO m 0 h 0 G 0 G 1 C 0 P 1 P 2 h 1 STABILITY REFERENCES POINTS AFTER MOVING DOWN**

**SHIP’S STABILITY VARIATIONS • MOVING CARGO m 0 h 0 G 0 P 1 C 0 P 2 STABILITY REFERENCES POINTS BEFORE MOVING UPWARD**

**SHIP’S STABILITY VARIATIONS h 0 > h 1 • MOVING CARGO P 1 m 0 P 2 G 1 G 0 h 0 C 0 h 1 STABILITY REFERENCES POINTS AFTER MOVING UPVARD**

**SHIP’S STABILITY VARIATIONS • LOADING CARGO m W 0 G 0 G 1 h 0 h 1 L 0 C 0**

**• SHIP’S STABILITY VARIATIONS FREE LIQUID AREA W 0 G 0 C 0 P 0 L 0**

**M Moment liquid • SHIP’S STABILITY VARIATIONS M Moment upserting FREE LIQUID AREA m W 0 W 1 G 0 C 0 P 1 C 1 P 1 L 0 L 1 Q**

**SHIP’S STABILITY VARIATIONS M 1 • FREE LIQUID AREA Y 1 Q 1 P 1 M 2 M 2 >M 1 Y 2 Q 2> Q 1 P 2**

**• M cargo SHIP’S STABILITY VARIATIONS HANGING CARGO Q l z W 0 W 1 L 1 M cargo = P cargo l z sin Q L 0 P**

**TRIM**

**Trim means different between draft fore TF and draft aft TAF W 1 W T AF T F L 1 L**

**4 3 2 1 7 6 5 T Af 9 m 8 2 SHIP’S TRIM DIAGRAM 3 4 5 6 7 8 9 T f m**

**D t 4000 3600 3200 2800 2400 1600 1200 -5 -4 SHIP’S TRIM DIAGRAM -3 -2 -1 0 0 1 2 X c m 3**

**SHIP’S STABILITY VARIATIONS**

**TRIM**

**Trim means different between draft fore TF and draft aft TAF W 1 W T AF P l x SHIP’S TRIM BEFORE SHIFTING CARGO Mdif D H T F L 1 L**

**SHIP’S STABILITY VARIATIONS**

**TRIM**

**Trim means different between draft fore TF and draft aft TAF W 1 d = P l x D H L W T AF1 T AF0 P l x P T F0 L SHIP’S TRIM AFTER SHIFTING CARGO L L 1 T F1 d**

**W O W 1 LIST Q L 1 Q L o**

**W O SHIP’S STABILITY VARIATIONS LIST P L o SHIP’S LIST BEFORE SHIFTING CARGO**

**W O W 1 SHIP’S STABILITY VARIATIONS LIST P l y P L 1 Q L o tg Q = P l y D h SHIP’S LIST AFTER SHIFTING CARGO**