ship stability theory
TRANSCRIPT
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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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EFFECT OF DENSITY ON SHIPS
VOLUME & DISPLACEMENT
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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EFFECT OF DENSITY ON SHIPS
VOLUME & DISPLACEMENT
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
EFFECT OF DENSITY ON SHIPS
VOLUME & DISPLACEMENT
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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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EFFECT OF DENSITY ON VOLUME & DISPLACEMENT
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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EFFECT OF DENSITY ON VOLUME & DISPLACEMENT
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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EFFECT OF DENSITY ON VOLUME & DISPLACEMENT
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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EFFECT OF DENSITY ON VOLUME & DISPLACEMENT
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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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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TRANSVERSE STABILITY
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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TRANSVERSE STABILITY
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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TRANSVERSE STABILITY
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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TRANSVERSE STABILITY
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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TRANSVERSE STABILITY
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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TRANSVERSE STABILITY
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
LONGITUDINAL STABILITY
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LONGITUDINAL STABILITY
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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LONGITUDINAL STABILITY
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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LONGITUDINAL STABILITY
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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LONGITUDINAL STABILITY
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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LONGITUDINAL STABILITY
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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LONGITUDINAL STABILITY
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LONGITUDINAL STABILITY
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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LONGITUDINAL STABILITY
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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LONGITUDINAL STABILITY
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