Ship STABILITY theory

8/10/2019 Ship STABILITY theory

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STABILITY

BASIC COARSE


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CHAPTER 3

A-DENSITY

B-RELATIVE DENSITY


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A-DENSITY

DENSITY :

DEFINDED AS THE MASS PER UNIT VOLUMEMEASURED INKG/M3 OR TON/M3 .

MASS IN KG OR TONS

DENSITY = ----------------------------------

kg/m3 or T/m3 VOLUME IN M3

VOLUME = L * B * D

(LENGTH * BREADTH * DEPTH )


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B-RELATIVE DENSITY

RELATIVE DENSITY:

DEFFINED AS THE RATIO BETWEEN THE DENSITYOF

ANY LIQUID TO THE DENSITY OF FRESH WATER.

R.D = DENSITY OF ANY LIQUID

DENSITY OF FRESH WATER

DENSITY OF FRESH WATER = 1000 KG/M3 OR 1.000 T/M3DENSITY OF SALT WATER = 1025 KG/M3 OR 1.025 T/M3


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CHAPTER 4

LAW OF FLOATATION


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LAW OF FLOATATION

LAW OF FLOATATION

THE MASS OF ANY SUBSTANCE IS EQUAL TO THEMASS OF THE WATER THE SUBSTANCE DISPLACES.

MASS OF SUBSTANCE = MASS OF WATER DISPLACED

AS THE SHIP MASS = DENSITY OF SHIP * SHIPS . VOLUME

( L * B * DEPTH)

AND

AS THE WATER MASS = DENSITY OF THE WATER * WATER VOLUMEDISPLACED BY THE PART UNDER WATER

( L * B * DRAFT )

SO SHIPS MASS = WATER DISPLACED MASS

DENSITY OF SHIP * DEPTH = DENSITY OF WATER * DRAFT


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LAW OF FLOATATION

THE WEIGHT OF ANY SHAPE IS ACTING ONLY AT A CERTAIN POINT WHICH ISCALLED CENTRE OF GRAVITY

CENTRE OF GRAVITY :

IS DEFINED AS A POINT WHERE THE SHIPS WEIGHT IS CONCENTRATED , THISFORCE IS ACTING DOWNWARD & THE POINT ALWAYS LIES AT THE DEPTH OF THE

SHAPEKG = DEPTH EXAMPLE DEPTH = 4m SO KG = 2m

DEPTH

W

G


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LAW OF FLOATATION

THE CENTRE OF BOUYANCY

IS DEFINED AS A POINT WHERE THE SHIPS BOUYANCY IS CONCENTRATED,

THIS FORCE IS ACTING UPWARD ,AND ALWAYS CENTERED AT

THE DRAFT . KB = DRAFT ,e.g; DRAFT = 4m , SO KB = 2m

B

W L

B

DRAFT


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LAW OF FLOATATION

W

KG = DEPTH

DEPTH

G

B

DRAFT KKB = DRAFT

B


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LAW OF FLOATATION

KG

DEFINED AS THE HEIGHT THAT LIES BETWEEN THE KEEL & THE CENTRE of

GRAVITY.

KBDEFINED AS THE HEIGHT THAT LIES BETWEEN THE KEEL & THE CENTRE OF

BOUYANCY.

REMARK ( B FORCE , G FORCE )

BOTH FORCES ACTS AGAINEST EACH OTHER S , IF THE G FORCE

INCREASED OVER THE B FORCE THE SHIP STARTS TO GO DOWN

;INCREASING THE SHIPS DRAFT BY THE DIFFRENCE IN FORCES .


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RESERVE BOUYANCY

DEFINED AS THE SPACE THAT LIES BETWEEN THE WATER SURFACE AND THE FIRST WATER

TIGHT INTEGRITY ( MAIN DECK).

Volume under water

Area under water

Reserve bouyancy

draft

depth

RESERVE BOUYANCY= DEPTH - DRAFT

OR

RESERVE BOUYANCY = VOLUME OF SHIP - VOLUME UNDER WATEROR

RESERVE BOUYANCY = AREA OF THE SHIP - AREA UNDER WATER


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EFFECT OF DENSITY ON SHIPS

VOLUME & DISPLACEMENT

A- BOX SHAPE VESSELS

B- SHIP SHAPE VESSELS

CHAPTER 5


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A-BOX SHAPED VESSELES

1-EFFECT OF DENSITY ON SHIPS VOLUME

2-EFFECT OF DENSITY ON SHIPDISPLACEMENT


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ANY BOX SHAPED VESSEL SAILS FROM ONE PORT TO ANOTHER CERTAIN

CHANGES OCCURES OVER THE SHIP, AS A RESULT OF THE EFFECT OF

DENSITY ON SHIPS VOLUME & DISPLACEMENT

AS WE KNOW THAT THE

A RELATION BETWEEN THE DENSITY & MASS WOULD BE ;DIRECT PROPORTION

DENSITY MASS ( DIRECT PROPORTION ) WHICH MEANS THAT

WHEN DENSITY DECREASES THE MASS DECREASES

WHEN DENSITY INCREASES THE MASS INCREASES

DENSITY = MASS kg

VOLUME


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A RELATION BETWEEN THE DENSITY & VOLUME WOULD BE ;INV. PROPORTION

DENSITY 1 / VOLUME ( INV. PROPORTION ) WHICH MEANS THAT

WHEN DENSITY DECREASES THE VOLUME INCREASES

WHEN DENSITY INCREASES THE VOLUME DECREASES

THE VOLUME IS THE SUM OF L * B * DRAFT ,

THE L & B NEVER CHANGE FROM PORT TO ANOTHER SO THE ONLYPARAMETER THAT CHANGES IS THE DRAFT ,THERFORE THE VOLUME

CHANGES ASWELL


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A-BOX SHAPED SHIPS

1-EFFECT OF DENSITY ON VOLUME


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EFFECT OF DENSITY ON VOLUME

LETS SAY A BOX SHAPED VESSEL DISPLACES 20,000 TONS SAILED

FROM PORT A HAS WATER DENSITY 1.OOO

TO PORT B HAS WATER DENSITY 1.025 ,

ACCORDING TO THE RELATION BETWEEN DENSITY AND VOLUME

INV.PROPORTIONS , WE DISCOVERS THAT AT PORT B, THE VOLUMEWILL DECREASES AS THE WATER DENSITY INCREASES ( 1.000 PORT A TO

1.025 PORT B ) ,

WHILE THE SHIP STILL DISPLACES THE SAME 20,000TONS

SINCE THE VOLUME = L * B * DRAFT ,

SO THE CHANGE IN THE VOLUME COMES FROM THE CHANGE IN THE

DRAFT


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EFFECT OF DENSITY ON VOLUME

SHIPS MASSAT PORT A = SHIPS MASSAT PORT B

WHERE THE MASS = DENSITY * VOLUME

( OLD DENSITY * OLD DRAFT ) = ( NEW DENSITY * NEW DRAFT )


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A-BOX SHAPED SHIPS

2-EFFECT OF DENSITY ON

DISPLACEMENT


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EFFECT OF DENSITY ON DISPLACEMENT

A BOX SHAPED VESSEL DISPLACES 20,000 TONS SAILED

FROM PORT A OF WATER DENSITY 1.OOO & DRAFT 7.0 mtrs

TO PORT B OF WATER DENSITY 1.025 ,

AS SHE ARRIVED TO PORT B , THE SHIPS DRAFT STAYED THE SAME 7.0 mtrs.

DESPITE THE DENSITY IS ALREADY CHANGED FROM 1.000 TO 1.025 ,

THAT MEANS A CHANGE OCCURRED ON THE SHIPS DISPLACEMENT (MASS)

YOU WILL FIND THE SHIP DISPLACEMENT BECAME 21,000 TONS AS EXAMPLE.

THE RELATION BETWEEN DENSITY & DISPLACEMENT (MASS) IS DIRECT

PROPORTIONS ,AS A RESULT THE DISPLACEMENT INCREASED WHENDENSITY

INCREASED ( 1.000 TO 1.025)


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EFFECT OF DENSITY ON DISPLACEMENT

SHIPS VOLUMEAT PORT A = SHIPS VOLUMEAT PORT B

THE SHIP DISPLACES THE SAME VOLUME OF WATER IN BOTH PORTS A & B

WHERE THE VOLUME =

OLD MASS NEW MASS

------------------------- = ----------------------

OLD DENSITY NEW DENSITY


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B- SHIP SHAPED VESSELS




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EFFECT OF DENSITY ON VOLUME & DISPLACEMENT

INORDER TO UNDER STAND THE EFFECT WE SHOULDVERY WELL UNDERSTAND THE PLYMSOL MARK (DRAFT MEASURES)

FREE BOARD

(RESERVE BOUYANCY)

54

WNAWinter

Summer

FWA Fresh

Tropical F

Tropical

230mm

300mm

540mm


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FWA ( FRESH WATER ALLOWANCE )DEFINED AS THE NUMBER OF MM THAT INCREASES OR DECREASES IN SHIPS MEAN

DRAFT WHEN THE SHIP SAILS FROM SALT WATER TO FRESH WATER & VISE VERSA

T P C ( TONS PER CENTIMETRE)DEFINED AS THE NUMBER OF TONS LOADED OR DISCHARGED INORDER TO CHANGE

SHIPS DRAFT 1 CM IN SALT WATER

FWA = DISPLACEMENT

4 * TPC


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DWA (DOCK WATER ALLOWANCE)DEFINED AS THE NUMBER OF MM THAT INCREASES OR DECREASES IN SHIPS MEAN

DRAFT WHEN THE SHIP SAILS FROM SALT WATER TO DOCK WATER & VISE VERSA.

Example : FWA 200mm (0.2mtrs) , DW DENSITY = 1.015

SO DWA = 0.2 * ( 10 ) = 0.08 mtrs ( 80 mm )

25

(1.025 - DWD)

DW A = FWA ----------------------

25


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IF THE SHIP SAILS FROM PORT A WHOSE WATER DENSITY IS 1.000 TO PORT B

WHOSE WATER DENSITY IS 1.025 ( THE DENSITY INCREASED) , SO ACCORDING TO

THE RELATION BETWEEN DENSITY & VOLUME.

DENSITY 1 / VOLUME ( INV. PROPORTION ) WHICH MEANS THAT

WHEN DENSITY DECREASES THE VOLUME INCREASES

WHEN DENSITY INCREASES THE VOLUME DECREASES

THE SHIPS DRAFT WILL DECREASES , THE VALUE OF DRAFT DECREASING EQUALS

THE FWA.

Eg. SHIP SHAPE V/L SAILED FROM PORT A WITH DENSITY 1.000 TO PORT B WITH

DENSITY 1.025 FWA 200MM .OLD DRAFT 7.0mtrs so the new draft will

decrease to 7.0 mt - FWA 200MM ( 20CM, 0.2mt )

7 - 0.2 = 6.8 mt ( NEW DRAFT )


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EXAMPLE

SHIP SHAPE V/L SAILED FROM PORT A WITH DENSITY 1.025 TO PORT B WITH

DENSITY 1.015 FWA 200MM .OLD DRAFT 7.0mtrs , DWA 200MM ,

SO THE NEW DRAFT WILL INCREASE ACCORDING TO THE INV. RELATION

BY THE VALUE OF THE DWA ( FROM SALT WATER DENSITY TO DOCK WATER

DENSITY ) ,

OLD DRAFT + DWA = NEW DRAFT

7.0 + 200mm( 0.2mtrs) = 7.2mtrs


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STATIC STABILITY

CHAPTER 6


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STATIC STABILITY

HEELING ,

IS THE ANGLE OCCURES WHEN IN THE SHIP WHEN HEELS TO ONE SIDE DUE TO

EXTERNAL FORCES (WIND,WAVES)

LIST,

IS THE ANGLE OCCURES IN THE SHIP WHEN HEELS TO ONE SIDE DUE TO

INTERNAL FORCES , LIST PORTSIDE OR LIST STRB SIDE.

( BALLAST,CARGO)

TRIM,

IS THE DIFFRENCE BETWEEN THE FORWARD DRAFT & THE AFT DRAFT.

TRIM COULD BE BY FORE ( FORWARD DRAFT LARGER THAN AFT DRAFT)

10 M FORE - 8.0 M AFT = 2.0 M BY FORE ( TRIM )

TRIM COULD BE BY AFT ( AFT DRAFT LARGER THAN FORE DRAFT)

10 M FORE - 15 M AFT = 5.0 M BY AFT ( TRIM )


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STATIC STABILITY

G.MKMKG

K

G

K

M

G

M

K

B B

B


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STATIC STABILITY

KM = KG + GM KM = KB + BM

KG = KB + BG

KG = KM - GM

GM = KM - KG

KB = DRAFT , KG = DEPTH

CENTRE OF BOUYANCY

ALWAYS MOVES TO THE HEELED SIDE TO BE CENTERED IN THE UNDERWATER VOLUME

KB =

DRAFT , KG = DEPTHKB = DRAFT , KG = DEPTH


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STATIC STABILITY

KG DEFINED AS THE HEIGHT BETWEEN THE KEEL & CENTRE OF GRAVITY

KM DEFINED AS THE HEIGHT BETWEEN THE KEEL & METACENTRE .THE HEIGHT

OF METACENTRE

GM DEFINED AS THE HEIGHT BETWEEN CENTRE OF GRAVITY & METACENTRE .

CALLED ( METACENTRIC HEIGHT)

GM COULD BE +VE ( G BELOW M ) STABLE SHIP

GM COULD BE -VE ( G ABOVE M ) UNSTABLE SHIP

G

M

M

+ VEGM -VE GM

G

W L


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STATIC STABILITY

METACENTRE POINTDEFINED AS THE POINT THAT EXISTS WHEN THE SHIP HEELS OR LISTS TO A SIDE ,

THIS POINT OCCURS WHEN THE LINE OF BOUYANCY THAT ACTS UPWARD

INTERSECT WITH THE CENTRE LINE.

B

K

W LG

B

W


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STATIC STABILITY

EQUILIBRIUM

STABLE SHIPSTABLE SHIP MEANS THAT THE SHIP HAS A +VE GM . AND WHEN HEELS OR LISTSA RIGHTING LEVER APPEARS , THE LEVER HAS A MOMENT TO RIGHTEN THE SHIP& BRINGS HER BACK TO THE UPRIGHT CONDOTION . THE STATICAL RIGHTENINGMOMENT IS THE SUM OF THE RIGHTENIG LEVER & THE SHIPS DISPLACEMENT.

THE RIGHTENING LEVER IS REPRESENTED BY GZ.

THE GZ THAT APPEARS , STARTS FROM THE GPOINT TO THE LINE OF BOUANCYMAKING A RIGHT ANGLE.

STATICAL RIGHTENIG MOMENT = RIGHTENING LEVER * DISPLACEMENT

RM ( TON METER) = GZ (mtrs) * ( tons )


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STATIC STABILITY

STABLE SHIP

STABLE SHIP B

W

w

k

B

G

M

B

W

B

B B

G

M

K

Z

G

STATICAL RIGHTENING MOMENT = GZ * DISPLACEMENT

A COUPLING IS SET TO BRING THE SHIP BACK TO UP RIGHT CONDOTION


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STATIC STABILITY

UNSTABLE SHIP

UNSTABLE SHIPMEANS THAT THE SHIP HAS A -VE GM ,THERFORE A CAPSIZING LEVER WILL

APPEARS ,WITH THE SHIPS DISPLACEMENT A CAPSIZING MOMENT OCCURES;

WHICH HEELS THE SHIP EVEN MORE TO THE HEELED OR THE LISTED SIDE.

STATICAL CAPSIZING MOMENT = - GZ * DISPLACEMENT

- RM = - GZ *


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STATIC STABILITY

UNSTABLE SHIP

UNSTABLE SHIP

W

K

B

M

G

B

W

K

B

M

GZ

B

B

W

GZ

STATICAL CAPSIZING MOMENT = - GZ * DISPLACEMENT

A COUPLING IS SET & INCREASES THE SHIPS HEEL OR LIST


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STATIC STABILITY

NEUTRAL SHIP

NEUTRAL SHIPDEFINED AS A SHIP HAS HER G POINT COINSIDE WITH THE M POINT

AS A RESULT NO LEVER APPEARS THERFORE NO MOMENT OCCURS ,&

NO COUPLING ARISES .THE SHIP STAYES HEELED . UNABLE TO BE UPRIGHT.

THE

K

B

M G

B

W

B B

K

G M

W

BB

W


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STATIC STABILITY

TENDER & STIFF SHIPS

TENDER SHIPA SHIP SAID TO BE TENDER WHEN SHE

HAS A

SMALL GM ,

WHEN SHE HEELS

GZ SMALL

CONSEQUNTLY

STATICAL RIGHTENING MOMENT IS ALSO SMALL.

THERFORE

PERIOD OF ROLLING IS LONG

EXAMPLE : PASSENGER SHIPS , CARGO SHIPS

K

G

M


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STATIC STABILITY

TENDER & STIFF SHIPS

STIFF SHIPA SHIP SAID TO BE STIFF WHEN SHE

HAS A

LARGE GM ,

WHEN SHE HEELS

GZ LARGE

CONSEQUNTLY

STATICAL RIGHTENING MOMENT IS ALSO LARGE.

THERFORE

PERIODE OF ROLLING IS SHORT

EXAMPLE : WAR SHIPS

K

G

M


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STATIC STABILITY

ANGLE OF LOLL ANGLE OF LOLL

THE ANGLE THAT APPEARS WHEN THE SHIP HEELS TO A SIDE WHILE THE SHIP HASAVE GM . A CAPSIZING MOMENT CREATED INCREASES THE HEELING ,

BY THAT TIME THE CENTRE OF BOUYANCY B STARTS TO MOVE TO THEHEELED SIDE UNTILL B REACHES A POINT JUST BELOW THE LINE OFGRAVITY. THE ANGLE WHERE THAT HAPPENS IS CALLED ANGLE OF LOLL .

WE NOTICE THAT THE SHIP AT THE ANGLE OF LOLL , HAS NO GZ, NO GM, NOMOMENTAT ALL.AS A RESULT THE SHIP STAYES ON THIS CONDITION ( HEELED)


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STATIC STABILITY

ANGLE OF LOLL

IF THE SHIP HEELED MORE CAUSE OF ANY REASON (WIND), THE CENTRE

OF BOUYANCY B MOVES FAR FURTHER AWAY IN THE HEELED SIDE, AS A

RESULT B IS NO MORE ACTING BELOW THE SAME LINE OF GRAVITY,

AND

A RIGHTNING MOMENT CREATED TO BRING BACK THE SHIP NOT TO THE

UPRIGHT CONDITION BUT TO THE ANGLE OF LOLL AGAIN. THE SHIPKEEPPS ROLLING AROUND THE ANGLE OF LOLL ,TILL THE PROBLEM IS

SOLVED.


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STATIC STABILITY

ANGLE OF LOLL

M

GZ

BB

K

B B

M G

B B

G Z

M

B

W

B

W

B

W

CAPSIZING

MOMENT

WINDWIND

WIND

RIGHTENING MOMENT

Fig.1 Fig.2

Fig. 3

LOLL


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STATIC STABILITY

CORRECTING ANGLE OF LOLL

INORDER TO CORRECT < OF LOLL WE MUST LOWER THE GBELOW M , PUTTING INTO CONSIDERATION THE SEQUENCE.

1. FILLING THE FULL BALLAST TANKS ( TO REMOVE FREE SURFACE)

2. LOWERING DOWN ANY UPPER LOADS ( CRANES , TOPSIDES TODOUBLEBOTTOM TANKS)

3. FILLING THE D.B TANKS IN THE HEELED SIDE4. THEN FILL THE D.B TANKS IN THE OTHER SIDE TO THE HEELED SIDE & THAT

SHOULD BE GRADUALLY.

WHY THE HEELED SIDE FIREST ?

AS FILLING THE TANKS IN THE HEELED SIDE THE G WILL MOVE UP SLOWLY&INCREASING LOLL ANGLE ;DUE TO FREE SURFACS ,BUT EVENTUALLY AFTER A

WHILE THE G STARTS TO MOVE DOWN ,ANGLE OF LOLL STARTS TO BE REDUCEDGRADUALLY ,UNTILL IT DISAPPEARS . G RETURNS BELOW M TO THE + VECONDITION CREATING ARIGHTENING MOMENT, MAKES THE SHIP BACK TO THEUPRIGHT CONDITION.


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STATIC STABILITY

CORRECTING ANGLE OF LOLL IF WE STARTS FILLING D.B TANKS IN THE HIGH SIDE , THE TANKS GETS

FILLED GRADUALLY ,AND OFCOARSE FREE SURFACE WILL MAKES THEG

MOVES MORE UP ,INCREASING THE HEEL;& ANGLE OF LOLL ; EVENTUALLY

THE FREE SURFACE EFFECT STARTS TO DISAPPEAR & THE SHIP STARTS TO

BE ADJUSTED & RETURNS TO THE UPRIGHT CONDITION CAUSE THE G

STARTS TO MOVE DOWN ,ANGLE OF LOLL DECREASES GRADUALLY , &THEN DISAPPEARS , & G TURNS TO BE BELOW THE M (+VE GM),A

RIGHTENING MOMENT IS CREATED BUT VERY STRONG ONE.

UNFORTUNATLY ,THE GZ CREATED IS VERY LARGE , THE RETURN WILL BE

VERY SEVERE ,STIFF AND IN A MATTER OF SECONDS; & LEADS TO A VERYDANGEROUS SITUATION TO THE SHIP.


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FINAL KG

CHAPTER


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FINAL KG

ANY SHIP DURING LOADING / DISCHARGING CARGO; THE CENTRE OF GRAVITY GSTARTS TO MOVE EITHER TOWARD OR AWAY FROM THE CENTRE OF GRAVITY gOF THEWEIGHTS LOADED / DISCHARGED .

As WE SEE(fig.1) GMOVED TO G RELATED TO g of the weight

As WE SEE(fig.2) GMOVED TO G RELATED TO g of the weight

K K

G G

G

g

g

G

Fig. 1 Fig.2


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FINAL KG

ACCORDING TO THE ILLUSTRATION , WE DISCOVER THAT THE G OF THE SHIP

KEEPS MOVING UP AND DOWN WITH THE g OF THE WEIGHTS LOADED

/DISCHARGED ,UNTILL IT IS SET IN A FINAL POSITION AFTER FINISHING THE

LOADING/DISCHARGING PROCESS.

SO ,WE HAVE AN INITIAL KG , ENDS UP BY FINAL KG .

THE FINAL KG LEADS TO THE FINAL GM.

FINAL GM = KM - FINAL KGFINAL GM = KM - FINAL KG


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FINAL KG

INORDER TO GET THE FINAL KG , EVERY WEIGHT HAS ITS Kg , THE G MOVES BY THE EFFECTOF THE MOMENT OCCURRED FROM THE Kg & w ,TILL GSTOPS AT A FINAL POSITION ( KG )

FINAL KG = TOTAL MOMENT 2000 = FINAL KG

TOTAL W 300

IF THE SHIPS KM = 8 m

so the final G.M = KM - FINAL KG

8 - 6.6 = final GM

w/tons Kg/m MOMENT/ ton m

100 10 1000

200 5.0 1000

Total w Total M

300 2000

6.6m

1.4m


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FINAL KG

GGIS THE MOVE OF G TO G DURING LOAD/DISCHLEADING TO THE FINAL KG, & FINAL GM

K

100 T

g

k

10m (kg)

200 T

g

k

5m (kg)

G

G

Initial KG

FINAL KG

M

Final GM

INITIAL GM


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GZ CURVES

CHAPTER


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GZ CURVES

GZ IS THE LEVER THAT OCCURES WHEN THE SHIP HEELS ,THE GZ LEVER ISRESPONSIBLE FOR RETURNING THE SHIP BACK TO THE UP RIGHT CONDITION.

THE LENGTH OF GZ LEVER DEPENDS ON TWO PARAMETERS ,

GM & ANGLE OF HEEL.

heel

GZ = GM * SIN

B

M

K

G

B

Z

G Z

M B

G C S


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GZ CURVES

GM

AS THE INCREASES , GZINCREASE TILL REACHES THE MAX THEN DROP DOWN AGAIN TOREACH THE VANISHING ANGLE.

THE RED LINE CALLED ARCHI . LINE ,FROM THIS LINE WE GET THE INITIAL GM OF THE SHIP. FROM 57.3 : EXTEND UP A LINE TO CUT THE ARCHI .LINE AT A POINT. FROM THIS POINT WE EXTENDA HORIZONTAL LINE TO READ THE GM, ON THE GZ SCALE .THE ARCHI LINE DRAWN AS ATANGENT FROM 0 AND SLOPE OF THE CURVE AS SHOWN BELOW.

3.9m

57.3

Vanishing angle91 :

Max GZ 40:Max GZ

ARCHI LINEGZ

10 20 30 40 50 60 70 80 90

GM 1.1 m

4

3

2

1

0

GZ CURVES


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GZ CURVES

STABLE SHIP

MAX GZ = 4.0 m AT 39.0: RANGE OF STABILITY = 090 : INITIAL GM = 1.3 m AT 57.3: VANISHING ANGLE = 90:

GZ

GM

GM

57,3

STABLE SHIP +VE GZ

10 20 30 40 50 60 70 80 90

4

1

2

0

3

1.3

GZ CURVES


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GZ CURVES

STATICAL MOMENT

IF THE SHIP DISPLACEMENT = 5000T THE MOMENT AT 25: WOULD BE GZ * W = MOMENT

3.0 * 5000 = 15000 Tm ( at 25: )

GZ

4

3

2

GM

1

57,32510 20 30 40 50 60 70 80 90

GZ CURVES


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GZ CURVES

UNSTABLE SHIP

GZ RANGE OF STABILITY 17 :--- 83: LOLL 17:

MAX GZ 3.8m at 43: VANISHING 83:

MAX GZ AT 43:

LOLL17:

43:

UNSTABLE SHIPVE GZ CURVE

83:

RANGE OF UNSTABILITY 0: --- 17:

< LOLL

GZ

10 20 30 40 50 60 70 80 900

-1

-2

1

2

3

4.0

GZ CURVES


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GZ CURVES

UNSTABLE SHIP

4_

3_

2_

1_

0 | | | | | | | | | |

-1

UNSTABLE SHIP -VE GZ

57.3

-2

-3

LOLL22:

GM3m

RANGE OF UNSTABILITY 0:--- 22:

RANGE OF STABILITY 22: -- 92:

INITIAL GM - 3 m

GZ

10 20 30 40 50 60 70 80 90 100


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FREE SURFACE

CHAPTER 7


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60/79


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FREE SURFACE

CONSEQUENTLY IT IS OBVIOUS THAT THE EFFECT OF THE FREE SURFACE ON THE

SHIPS STABILITY IS SIMMILLAR AS SHIFTING A LOAD VERTICALLY UP.

THE RIGHTENING MOMENT IS AFFECTED FROM THE FREE SURFACE ,AS THE G

MOVES HORIZONTALLY TO G & PARALLEL TO g g1 , THAT MEANS THE GZ WILLBE REDUCED TO GZ AND CONSEQUENTLY THE RIGHTENING MOMENT WILL ALSO

BE REDUCED . RM = GZ * W

IN PRESENCE OF FREE SURFACE ,THE EFFECT RM = GZ*W

AS THE G ALSO MOVES UP VERTICALLY TO G1 , GM REDUCED BY THE VALUE OFTHE MOVE OF G TO G1 & THAT IS CALLED THE LOSS IN GM (LOSS IN STABILITY) ,

THE NEW IS G1M


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FREE SURFACE

SUMMARY1. FREE SURFACE COMES FROM FULL TANKS

2. FREE SURFACE LEADS TO LOSS IN SHIPS STABILITY

(LOSS IN GM)

3. FREE SURFACE REDUCES THE SHIPS RIGHTENING MOMENT4. FREE SURFACE REDUCES THE GZ

5. FREE SURFACE EFFECT ON SHIPS STABILITY IS EQUIVILANT TO THE EFFECT OF

SHIFTING A LOAD VERTICALLY UPWARD .

6. FREE SURFACE MAKES THE LIQUID IN TANK TO LEAN TO THE HEELED SIDE , &

ADDS AN EXTRA HEELING MOMENT(CAPSIZING) ,I.E REDUCES THERIGHTENING MOMENT WHICH MAKES THE SHIP TO HEEL WITH A LARGER


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TRANSVERSE STABILITY


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LIST

LIST IS THE ANGLE THAT OCCURES WHEN THE SHIP LEAN TO EITHER SIDEPORT OR STRB AS ARESULT OF THE EFFECT OF AN INTERNAL FORCE SUCH AS

BALLAST TANKS , CARGO DISTRIBUTION / SHIFTING .

DURING LOADING /DISCHARGING A SHIP, THE WEIGHTS ADDED/REMOVED FROMTHE SHIPS SIDES LEADS TO LIST HER TO EITHER SIDE.

THE LIST THAT OCCURES DEPENDSON THE MOMENTTHAT EXISTS FROM THE SUM

OF WEIGHTS ADDED /REMOVED & THERE DISTANCE FROM THE CENTRE LINE.

LIST MOMENT = W * d ( distance from centre line)



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LIST

The IDEA IS EQUIVILANT FROM THE point of VIEW OF A SIMPLE BALANCE.

2OO

1001OO

3OO3OO

5O

d d

Fig .1

AS THE Fig . 1 SHOWS, EVERY WEIGHT IS FAR FROM THE CENTRE BY d ,

INORDER TO KNOW WHICH SIDE IS HEAVIER AND LEADS THE BALANCE TO

LEAN ,WE SHOULD GET THE TOTAL MOMENT PORT & TOTAL MOMENT

STRB ,MOMENT = W * D



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LIST

The SHIP LIST IS VERY SIMILLAR TO THE LAST EXAMPLE CONCEPT.

STBPORT

d d

dd

d d

d

dd d

100 50

200

100

150

300

200

150

50

300

SO ,EACH WEIGHT IN THE SHIP IS FAR FROM THE CENTRE LINE BY DISTANCE

d

The SHIP WILL LEAN TO ONE SIDE ACCORDING TO THE MOMENT OF EACH

SIDE.MOMENT = W * D



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LIST

A DEEPER VIEW TOWARD THE EFFECT OVER THE SHIPS STBILITY GMTHE GMOVES TO THE WEIGHT g

FINALLY THE SHIPS G

GETS OUT OF THE CENTRE

LINE TO THE SIDE WHICH

HAS THE BIGGER MOMENT;AS A RESULT THE SHIP LEANS

TO THAT SIDE, & STOPS WHEN THE B

COMES JUST UNDER THE G ,AND ACTS

ON THE SAME LINE OF WORK.

SO THE SHIPS G, SETTELED AT G ,

TAN = GG GM

IS THE LISTING ANGLE

K

G G

M

BB

W

B

G G

M



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LIST

MomentStrb

Momentport

D ( gg)Distance from centre line

w

5001050

400020200

150010150

15005300

5005100

100010100

10005200

150010150

250550

300010300

800067501600

1250 strbFINAL GG1600ton



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LIST

LISTING MOMENT = 1250 STRB

TOTAL WEIGHT = 1600 TON

FINAL GG = TOTAL MOMENT 1250 = 0.781 mtrs.

TOTAL WEIGHT 1600

IF THE FINAL GM = 5.5 mtrs

TAN = GG0.781 = 8: strbGM 5.50

G G

M

0.781

5.5

8:


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LONGITUDINAL STABILITY

TRIMCHAPTER



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TRIM

TRIM IS THE DIFFERENCE BETWEEN THE AFT DRAFT & THE FORE DRAFT. TRIMCOULD BE BY AFT OR BY FORE.

IF THE FOR & AFT DRAFT WERE EQUAL & HAD NO DIFFERENCE ,THEN THE SHIP

SAID TO BE ON AN EVEN KEEL.

LBP

L1L2

LBP IS THE LENGTH BETWEEN PERPENDICULAR MIDSHIP

L1 DISTANCE FROM AFT B. TO MID SHIP,CF

L2 DISTANCE FROM FORE B. TO MID SHIP,CF



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TRIM

IF ANY LOADS ADDED OR REMOVED FROM THE SHIP ,THERE WILL BE AN EFFECT

ON THE SHIPS DRAFTS & CONSEQUENTLY ON THE TRIM.

THE LOADS WILL CHANGE THE DRAFTS AFT & FORE BY THE SAME VALUE,THAT

ONLY HAPPENS IF THE CENTRE OF FLOATATION IS AMIDSHIP,IF NOT ,THE CHANGE

WILL DEPEND ON THE CHANGE IN TRIM OCCURRED.& L1 ,L2 & L.

LBP

L1L2

DRAFT

FORE

DRAFT

AFTCF

L



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TRIM

WHEN A LOAD IS ADDED ,THE GWILL MOVE TOWARD THE g of the weight,making

THE SHIP TO LEAN FORWARD .THE SHIP STOPS LEANING FORWARD ONCE B MOVES

& REACH JUST BELOW THE G , WHICH MEANS BOTH G & B ACTS AGAIN ON THE

SAME LINE OF WORK. THE FINAL GG ( DISTANCE BETWEEN G &G) COULD BE

CALCULATED FROM THE FINAL MOMENTS OF THE WEIGHTS & TOTAL WEIGHTS.

W

GG

BB

GML



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TRIM

CENTRE OF FLOATATION IS THE CENTRE WHERE THE LINES OF WATERINTERSECTS . THE SHIP TRIM LONGITUDINALY AROUND THIS POINT. THE DRAFT

AT THIS POINT IS CONSTANT.

LBP

L1L2

CFNEW

DRAFT

AFTNEW

DRAFT

FORE



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TRIM

IF A LOAD IS ADDED AFT ,THE SHIPS DRAFT AFT WILL BE INCREASED WHILE THE

SHIPS DRAFT FORE DECREASES, AS SHOWN IN THE fig. 1 BELOW. THE EFFECT OF

THE WEIGHT OVER THE SHIPS TRIM COMES FROM THE MOMENT IT MAKES.

TRIMMING MOMENT IS THE MOMENTTO CHANGE THE SHIPS TRIM,& IT IS THE

SUM OF THE W & DISTANCE OF WFROM CF.

trimming moment = _w * d MEASURED IN TON METERW

LBP

L1L2

CFNEW

DRAFT

AFTNEW

DRAFT

FORE

W

Fig.1

d


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TRIM

THE TOTAL CHANGE IN TRIM IN CM ,WILL BE DISTRIBUTED BETWEEN THE DRAFTS

FORE & AFT. IF THE CF OF THE SHIP IS COINSIDE WITH THE MID SHIP POINT ,THE

CHANGE IN TRIM WILL BE DIVIDED EQUALLY ON BOTH DRAFTS.

EXAMPLE . CHANGE IN TRIM = 6 CM CF MID SHIP

SO DRAFT AFT = +3 CM DRAFT FORE = - 3 CM

LBP

L1L2

CFW

Fig.1

d



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TRIM

THE TOTAL CHANGE IN TRIM IN CM ,WILL BE DISTRIBUTED BETWEEN THE DRAFTS

FORE & AFT. IF THE CF OF THE SHIP IS NOT IN THE MID ,THE CHANGE IN TRIM

WILL BE DISTRIBUTED BETWEEN THE DRAFTS BY THE FOLLOWING.

DRAFT FORE = L2 * CHANGE OF TRIM (L2 DIST FROM CF TO FORE B )

L ( L1 DIST FROM CF TO AFT B)

DRAFT AFT = L1_ * CHANGE OF TRIM ( L IS THE LBP )

L

L

L1L2

CFNEW

DRAFT

AFTNEW

DRAFT

FORE

W

Fig.1

d



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TRIM

THE ADDED /DISCHARGED WEIGHT ALSO HAS AN EFFECT OVER THE SHIP , THE EFFECT

APPEARS OVER THE SHIPS MEAN DRAFT CALLED BODILY SINKAGE/RISE ,THIS

CHANGE ADDED OR REMOVED TO BOTH DRAFTS FORE & AFT.

IF A WEIGHT ADDED THE EFFECT CALLED BODILY SINKAGE = _W _

IF A WEIGHT DISCH. THE EFFECT CALLED BODILY RISE TPC

L

L1L2

CFNEW

DRAFT

AFTNEW

DRAFT

FORE

W

Fig.1

d

Documents

Ship STABILITY theory