STABILITY
BASIC COARSE
CHAPTER 3
A-DENSITY
B-RELATIVE DENSITY
A-DENSITY
• DENSITY :
DEFINDED AS THE MASS PER UNIT VOLUME MEASURED IN
KG/M3 OR TON/M3 .
DENSITY
=
kg/m3 or T/m3
VOLUME = L * B * D
(LENGTH * BREADTH * DEPTH )
MASS IN KG OR TONS
---------------------------------VOLUME IN M3
B-RELATIVE DENSITY
RELATIVE DENSITY:
DEFFINED AS THE RATIO BETWEEN THE DENSITY OF
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/M3
DENSITY OF SALT WATER = 1025 KG/M3 OR 1.025 T/M3
CHAPTER 4
LAW OF FLOATATION
LAW OF FLOATATION
• LAW OF FLOATATION
THE MASS OF ANY SUBSTANCE IS EQUAL TO THE
MASS OF THE WATER THE SUBSTANCE DISPLACES.
MASS OF SUBSTANCE
AS THE SHIP MASS
=
= MASS OF WATER DISPLACED
DENSITY OF SHIP * SHIPS . VOLUME
( L * B * DEPTH)
AND
AS THE WATER MASS = DENSITY OF THE WATER * WATER VOLUME
DISPLACED BY THE PART UNDER WATER
SO
SHIPS MASS
DENSITY OF SHIP * DEPTH
( L * B * DRAFT )
= WATER DISPLACED MASS
= DENSITY OF WATER * DRAFT
LAW OF FLOATATION
•
THE WEIGHT OF ANY SHAPE IS ACTING ONLY AT A CERTAIN POINT WHICH IS
CALLED CENTRE OF GRAVITY
CENTRE OF GRAVITY :
IS DEFINED AS A POINT WHERE THE SHIPS WEIGHT IS CONCENTRATED , THIS
FORCE IS ACTING DOWNWARD & THE POINT ALWAYS LIES AT ½ THE DEPTH OF THE
SHAPE
KG = ½ DEPTH
EXAMPLE DEPTH = 4m SO KG = 2m
DEPTH
G
₀
W
LAW OF FLOATATION
• THE CENTRE OF BOUYANCY
• IS DEFINED AS A POINT WHERE THE SHIP’S BOUYANCY IS CONCENTRATED,
THIS FORCE IS ACTING UPWARD ,AND ALWAYS CENTERED AT
½ THE DRAFT . KB = ½ DRAFT ,e.g; DRAFT = 4m , SO KB = 2m
B’
W
L
B
₀
DRAFT
LAW OF FLOATATION
W
KG = ½ DEPTH
DEPTH
• G
• B
K
DRAFT
KB = ½ DRAFT
B
LAW OF FLOATATION
KG
DEFINED AS THE HEIGHT THAT LIES BETWEEN THE KEEL & THE CENTRE of
GRAVITY.
KB
DEFINED 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 .
RESERVE BOUYANCY
DEFINED AS THE SPACE THAT LIES BETWEEN THE WATER SURFACE AND THE FIRST WATER
TIGHT INTEGRITY ( MAIN DECK).
RESERVE BOUYANCY =
DEPTH - DRAFT
OR
RESERVE BOUYANCY = VOLUME OF SHIP - VOLUME UNDER WATER
OR
RESERVE BOUYANCY = AREA OF THE SHIP - AREA UNDER WATER
Reserve bouyancy
depth
Volume under water
Area under water
draft
EFFECT OF DENSITY ON SHIP’S
VOLUME & DISPLACEMENT
A- BOX SHAPE VESSELS
B- SHIP SHAPE VESSELS
CHAPTER 5
A-BOX SHAPED VESSELES
1-EFFECT OF DENSITY ON SHIP’S VOLUME
2-EFFECT OF DENSITY ON SHIP’DISPLACEMENT
EFFECT OF DENSITY ON SHIP’S
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 SHIP’S VOLUME & DISPLACEMENT
AS WE KNOW THAT THE
DENSITY
= MASS kg
VOLUME
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
EFFECT OF DENSITY ON SHIP’S
VOLUME & DISPLACEMENT
•
A RELATION BETWEEN THE DENSITY & VOLUME WOULD BE ; INV. PROPORTION
DENSITY 1 / ∞ VOLUME ( INV. PROPORTION ) WHICH MEANS THAT
WHEN
WHEN
DENSITY DECREASES THE VOLUME INCREASES
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 ONLY
PARAMETER THAT CHANGES IS THE DRAFT ,THERFORE THE VOLUME
CHANGES ASWELL
A-BOX SHAPED SHIPS
1-EFFECT OF DENSITY ON VOLUME
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 VOLUME
WILL 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
EFFECT OF DENSITY ON VOLUME
SHIP’S MASS AT PORT A
=
SHIP’S MASS AT PORT B
WHERE THE MASS = DENSITY * VOLUME
( OLD DENSITY * OLD DRAFT )
= ( NEW DENSITY * NEW DRAFT )
A-BOX SHAPED SHIPS
2-EFFECT OF DENSITY ON
DISPLACEMENT
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 SHIP’S 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 WHEN DENSITY
INCREASED ( 1.000 TO 1.025)
EFFECT OF DENSITY ON DISPLACEMENT
•
SHIP’S VOLUME AT PORT A
=
SHIP’S VOLUME AT PORT B
THE SHIP DISPLACES THE SAME VOLUME OF WATER IN BOTH PORTS A & B
WHERE THE VOLUME =
OLD MASS
------------------------OLD
DENSITY
NEW MASS
=
---------------------NEW DENSITY
B- SHIP SHAPED VESSELS
EFFECT OF DENSITY ON SHIP’S
VOLUME & DISPLACEMENT
EFFECT OF DENSITY ON VOLUME & DISPLACEMENT
• INORDER TO UNDER STAND THE EFFECT WE SHOULD
VERY WELL UNDERSTAND THE PLYMSOL MARK (
DRAFT MEASURES)
FREE BOARD
230mm
(RESERVE BOUYANCY )
Tropical
Tropical F
FWA
Fresh
Summer
54
300mm
540mm
Winter
WNA
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
FWA = DISPLACEMENT
4 * TPC
• 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
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.
DW A =
FWA
(1.025 - DWD)
---------------------25
Example : FWA 200mm (0.2mtrs) , DW DENSITY = 1.015
SO DWA = 0.2 * ( 10 ) = 0.08 mtrs ( 80 mm )
25
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 )
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
STATIC STABILITY
CHAPTER 6
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 )
STATIC STABILITY
M
M
G
G
B
KG
K
B
KM
K
B
G.M
K
STATIC STABILITY
•
•
•
•
•
KM
KM
KG
KG
GM
=
=
=
=
=
KG
KB
KB
KM
KM
+ GM
+ BM
+ BG
- GM
- KG
KB =
½ DRAFT , KG = ½ DEPTHKB = ½ DRAFT , KG = ½ DEPTH
• KB = ½ DRAFT , KG = ½ DEPTH
CENTRE OF BOUYANCY
ALWAYS MOVES TO THE HEELED SIDE TO BE CENTERED IN ½ THE UNDER
WATER VOLUME
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
W
M•
G•
G•
M•
+ VEGM
-VE GM
L
STATIC STABILITY
• METACENTRE POINT
DEFINED 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
W
G
•
L
B’
K
W
STATIC STABILITY
EQUILIBRIUM
• STABLE SHIP
STABLE SHIP MEANS THAT THE SHIP HAS A +VE GM . AND WHEN HEELS OR LISTS
A RIGHTING LEVER APPEARS , THE LEVER HAS A MOMENT TO RIGHTEN THE SHIP
& BRINGS HER BACK TO THE UPRIGHT CONDOTION . THE STATICAL RIGHTENING
MOMENT IS THE SUM OF THE RIGHTENIG LEVER & THE SHIPS DISPLACEMENT.
STATICAL RIGHTENIG MOMENT = RIGHTENING LEVER * DISPLACEMENT
RM ( TON METER)
= GZ (mtrs)
*
∆ ( tons )
THE RIGHTENING LEVER IS REPRESENTED BY GZ.
THE GZ THAT APPEARS , STARTS FROM THE G POINT TO THE LINE OF
MAKING A RIGHT ANGLE.
BOUANCY
STATIC STABILITY
STABLE SHIP
• STABLE SHIP
B
B
G
B
W
M
M •
G •
B •
G •
B•
•
Z
B’
k
K
w
W
STATICAL RIGHTENING MOMENT = GZ * DISPLACEMENT
A COUPLING IS SET TO BRING THE SHIP BACK TO UP RIGHT CONDOTION
STATIC STABILITY
UNSTABLE SHIP
• UNSTABLE SHIP
MEANS THAT THE SHIP HAS A -VE GM ,THERFORE A CAPSIZING LEVER WILL
APPEARS ,WITH THE SHIP’S DISPLACEMENT A CAPSIZING MOMENT OCCURES;
WHICH HEELS THE SHIP EVEN MORE TO THE HEELED OR THE LISTED SIDE.
STATICAL CAPSIZING MOMENT =
- RM
=
- GZ
- GZ
* DISPLACEMENT
*
∆
STATIC STABILITY
UNSTABLE SHIP
• UNSTABLE SHIP
B
B
Z
B
G
G•
M•
Z• • G
W
M•
B•
K
W
B•
K
W
STATICAL CAPSIZING MOMENT = - GZ * DISPLACEMENT
A COUPLING IS SET & INCREASES THE SHIPS HEEL OR LIST
STATIC STABILITY
NEUTRAL SHIP
• NEUTRAL SHIP
DEFINED 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.
B
B
M
B
G • M
G
W
B
K
W
THE
B • • B’
K
W
STATIC STABILITY
TENDER & STIFF SHIPS
• TENDER SHIP
A 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
M
G
K
STATIC STABILITY
TENDER & STIFF SHIPS
• STIFF SHIP
A 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
M
G
K
STATIC STABILITY
ANGLE OF LOLL
• ANGLE OF LOLL
THE ANGLE THAT APPEARS WHEN THE SHIP HEELS TO A SIDE WHILE THE SHIP HAS
A –VE GM . A CAPSIZING MOMENT CREATED INCREASES THE HEELING ,
BY THAT TIME THE CENTRE OF BOUYANCY B STARTS TO MOVE TO THE
HEELED SIDE UNTILL B REACHES A POINT JUST BELOW THE LINE OF
GRAVITY. 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, NO
MOMENT AT ALL.AS A RESULT THE SHIP STAYES ON THIS CONDITION ( HEELED)
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 SHIP
KEEPPS ROLLING AROUND THE ANGLE OF LOLL ,TILL THE PROBLEM IS
SOLVED.
STATIC STABILITY
ANGLE OF LOLL
B
B
LOLL
WIND
WIND
Z• • G
M G
•
M •
CAPSIZING
MOMENT
B•
B
•
B’
K
Fig.1
B’
•
B
W
Fig.2
M•
G • •Z
WIND
B•
RIGHTENING MOMENT
Fig.
3
•
B’
W
W
STATIC STABILITY
CORRECTING ANGLE OF LOLL
INORDER TO CORRECT < OF LOLL WE MUST LOWER THE G
BELOW M , PUTTING INTO CONSIDERATION THE SEQUENCE.
1.
2.
3.
4.
FILLING THE ½ FULL BALLAST TANKS ( TO REMOVE FREE SURFACE)
LOWERING DOWN ANY UPPER LOADS ( CRANES , TOPSIDES TODOUBLE
BOTTOM TANKS)
FILLING THE D.B TANKS IN THE HEELED SIDE
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 REDUCED
GRADUALLY ,UNTILL IT DISAPPEARS . G RETURNS BELOW M TO THE + VE
CONDITION CREATING A RIGHTENING MOMENT, MAKES THE SHIP BACK TO THE
UPRIGHT CONDITION.
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 THE G
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 VERY
DANGEROUS SITUATION TO THE SHIP.
FINAL KG
CHAPTER
FINAL KG
•
ANY SHIP DURING LOADING / DISCHARGING CARGO; THE CENTRE OF GRAVITY G
STARTS TO MOVE EITHER TOWARD OR AWAY FROM THE CENTRE OF GRAVITY g OF THE
WEIGHTS LOADED / DISCHARGED .
•
•
As WE SEE(fig.1) G MOVED TO G’ RELATED TO g of the weight
As WE SEE(fig.2) G MOVED TO G’ RELATED TO g of the weight
G’
g
G
G
G’
»
g
K
K
Fig. 1
Fig.2
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
GMGM
= KM
FINAL
= KM- -FINAL
FINAL KG
KG
FINAL KG
•
INORDER TO GET THE FINAL KG , EVERY WEIGHT HAS ITS Kg , THE G MOVES BY THE EFFECT
OF THE MOMENT OCCURRED FROM THE Kg & w ,TILL G STOPS AT A FINAL POSITION ( KG )
w/tons
Kg/m
MOMENT/ ton m
100
10
1000
200
5.0
1000
Total w
Total M
300
2000
FINAL KG’ = TOTAL MOMENT 2000 = FINAL KG’
TOTAL W
300
IF THE SHIP’S KM = 8 m
so the final G’.M = KM - FINAL KG’
8 6.6
= final G’M
6.6m
1.4m
FINAL KG
• GG’IS THE MOVE OF G TO G’ DURING
LOAD/DISCH
100 T
LEADING TO THE FINAL KG, & FINAL GM
g
M
Final G’M
G’
200 T
INITIAL GM
g
10m (kg)
G
FINAL KG
5m (kg)
Initial KG
k
K
k
GZ CURVES
CHAPTER
GZ CURVES
•
•
GZ IS THE LEVER THAT OCCURES WHEN THE SHIP HEELS ,THE GZ LEVER IS
RESPONSIBLE FOR RETURNING THE SHIP BACK TO THE UP RIGHT CONDITION.
THE LENGTH OF GZ LEVER DEPENDS ON TWO PARAMETERS ,
GM & ANGLE OF HEEL.Ѳ
GZ = GM * SIN Ѳ
B’
M
Ѳ
heel
M
•
G ••Z
B
G
Z
K
B’
GZ CURVES
GM
•
•
AS THE Ѳ INCREASES , GZ INCREASE TILL REACHES THE MAX THEN DROP DOWN AGAIN TO
REACH THE VANISHING ANGLE.
THE RED LINE CALLED ARCHI . LINE ,FROM THIS LINE WE GET THE INITIAL GM OF THE SHIP. FROM
Ѳ 57.3 ⁰ EXTEND UP A LINE TO CUT THE ARCHI .LINE AT A POINT. FROM THIS POINT WE EXTEND
A HORIZONTAL LINE TO READ THE GM, ON THE GZ SCALE .THE ARCHI LINE DRAWN AS A
TANGENT FROM 0 AND SLOPE OF THE CURVE AS SHOWN BELOW.
4
3.9m
Ѳ 40⁰
Max GZ
Max GZ
3
GZ
ARCHI LINE
2
GM 1.1 m
1
0
Vanishing angle
91 ⁰
10
20
30
40
50
60
57.3
70
80
90
GZ CURVES
STABLE SHIP
•
•
MAX GZ
INITIAL GM
GZ
= 4.0 m AT Ѳ 39.0⁰
= 1.3 m AT Ѳ 57.3⁰
RANGE OF STABILITY = 0—90 ⁰
VANISHING ANGLE = 90⁰
STABLE SHIP +VE GZ
4
3
2
GM
1.3
GM
1
0
10
20
30
40
50 57,3 60
70
80
90
GZ CURVES
STATICAL MOMENT
•
•
IF THE SHIP DISPLACEMENT = 5000T THE MOMENT AT 25⁰ WOULD BE
GZ * W = MOMENT
3.0 * 5000 = 15000 Tm ( at 25⁰ )
GZ
4
3
2
GM
1
10
20 25 30
40
50
57,360
70
80
90
GZ CURVES
UNSTABLE SHIP
GZ
RANGE OF STABILITY 17 ⁰--- 83⁰
Ѳ LOLL 17⁰
MAX GZ 3.8m at Ѳ 43⁰ VANISHING Ѳ 83⁰
4.0
MAX GZ AT 43⁰
UNSTABLE SHIP –VE GZ CURVE
3
GZ
2
< LOLL
1
0
10
-1
20
Ѳ LOLL
17⁰
30
40
50
43⁰
60
70
80
83⁰
90
-2
RANGE OF UNSTABILITY 0⁰ --- 17⁰
GZ CURVES
UNSTABLE SHIP
GZ
UNSTABLE SHIP -VE GZ
4_
RANGE OF UNSTABILITY 0⁰--- 22⁰
RANGE OF STABILITY 22⁰ -- 92⁰
INITIAL GM - 3 m
3_
2_
Ѳ LOLL
22⁰
1_
57.3
0
-1
|
|
|
|
|
|
|
|
|
|
10
20
30
40
50
60
70
80
90
100
-2
-3
GM – 3m
FREE SURFACE
CHAPTER 7
FREE SURFACE
• FREE SURFACE
IS DEFINED AS THE SURFACE THAT CAN MOVE FREELY FROM ONE SIDE TO
ANOTHER FREELY , EXAMPLE A TANK ½ FULL OF BALLAST .
THE FREE SURFACE HAS A NEGATIVE EFFECT OVER THE SHIP’S STABLE CONDITION,
MORE CLEARLY THE FREE SURFACE LEADS TO LOSS IN THE G M , WHICH MEANS
THAT IT COULD REDUCES THE GM TO THE EXTENT OF CONVERTING THE +VE GM
TO -VE GM ( STABLE SHIP TO UNSTABLE SHIP ),SPECIALLY IF THE SHIP STARTED
HER VOYAGE WITH A SMALL INITIAL G.M , AS A RESULT THE SHIP CAN EASILY
CAPSIZE & SINKS.
FREE SURFACE
•
THE FREE SURFACE REDUCES THE SHIP RIGHTENING MOMENT BY REDUCING THE
GZ LEVER, THE LEVER WHICH USED TO BRING THE SHIP BACK TO THE UPRIGHT
CONDITION .
• , THE FREE SURFACE MAKES AN EXTRA CAPSIZING MOMENT OVER THE SHIP,
AS A RESULT OF THE EXTRA WEIGHT ADDED FROM THE LIQUID IN THE ½ FULL
TANK IN THE HEELED SIDE.
g moved to g1
ALSO // G MOVED TO G’
AS LIQUIDE HEELED
M
G’Z < GZ
NEW MOMENY< OLD MOMENT
NEW G1M < OLD GM
GG1 = LOSS IN GM
G1
G
B
Z1
G’
Z
B’
FREE SURFACE
•
CONSEQUENTLY IT IS OBVIOUS THAT THE EFFECT OF THE FREE SURFACE ON THE
SHIP’S 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 WILL
BE REDUCED TO G’Z AND CONSEQUENTLY THE RIGHTENING MOMENT WILL ALSO
BE REDUCED .
RM = GZ * W
IN PRESENCE OF FREE SURFACE ,THE EFFECT
RM = G’Z *W
•
AS THE G ALSO MOVES UP VERTICALLY TO G1 , GM REDUCED BY THE VALUE OF
THE MOVE OF G TO G1 & THAT IS CALLED THE LOSS IN GM (LOSS IN STABILITY) ,
THE NEW IS G1M
FREE SURFACE
• SUMMARY
1.
2.
3.
4.
5.
6.
FREE SURFACE COMES FROM ½ FULL TANKS
FREE SURFACE LEADS TO LOSS IN SHIPS STABILITY
(LOSS IN GM)
FREE SURFACE REDUCES THE SHIPS RIGHTENING MOMENT
FREE SURFACE REDUCES THE GZ
FREE SURFACE EFFECT ON SHIPS STABILITY IS EQUIVILANT TO THE EFFECT OF
SHIFTING A LOAD VERTICALLY UPWARD .
FREE SURFACE MAKES THE LIQUID IN TANK TO LEAN TO THE HEELED SIDE , &
ADDS AN EXTRA HEELING MOMENT(CAPSIZING) ,I.E” REDUCES THE
RIGHTENING MOMENT “WHICH MAKES THE SHIP TO HEEL WITH A LARGER Ѳ
TRANSVERSE STABILITY
LIST
CHAPTER
TRANSVERSE STABILITY
LIST
• LIST IS THE ANGLE THAT OCCURES WHEN THE SHIP LEAN TO EITHER SIDE
PORT 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 FROM
THE SHIPS SIDES LEADS TO LIST HER TO EITHER SIDE.
THE LIST THAT OCCURES DEPENDS ON THE MOMENT THAT EXISTS FROM THE SUM
OF WEIGHTS ADDED /REMOVED & THERE DISTANCE FROM THE CENTRE LINE.
LIST MOMENT = W * d ( distance from centre line)
TRANSVERSE STABILITY
LIST
• The IDEA IS EQUIVILANT FROM THE point of VIEW OF A SIMPLE BALANCE.
d
d
2OO
3OO
3OO
1OO
100
5O
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
TRANSVERSE STABILITY
LIST
•
The SHIP LIST IS VERY SIMILLAR TO THE LAST EXAMPLE CONCEPT.
PORT
STB
100
d
200
50
d
200
d
150
d
d
150
d
50
d
300
d
300
d
100
d
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
TRANSVERSE STABILITY
LIST
• A
DEEPER VIEW TOWARD THE EFFECT OVER THE SHIP’S STBILITY “GM”
B
THE G MOVES TO THE WEIGHT g
FINALLY THE SHIP’S 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 SHIP’S G , SETTELED AT G’ ,
M
Ѳ
G
B
B’
K
TAN Ѳ = GG ‘
GM
Ѳ IS THE LISTING ANGLE
G’
M
G
W
Ѳ
G’
TRANSVERSE STABILITY
LIST
w
D ( gg’)
Distance from centre line
50
10
500
200
20
4000
150
10
1500
300
5
1500
100
5
500
100
10
1000
200
5
1000
150
10
1500
50
5
250
300
10
3000
1600
1600ton
Moment
port
6750
FINAL GG’
Moment
Strb
8000
1250 strb
TRANSVERSE STABILITY
LIST
• LISTING MOMENT = 1250 STRB
• TOTAL WEIGHT = 1600 TON
• FINAL GG’ = TOTAL MOMENT
•
TOTAL WEIGHT
• IF THE FINAL GM = 5.5 mtrs
1250 = 0.781 mtrs.
1600
M
TAN Ѳ = GG’ 0.781 = 8⁰ strb
GM 5.50
8⁰
5.5
G
G’
0.781
LONGITUDINAL STABILITY
TRIM
CHAPTER
LONGITUDINAL STABILITY
TRIM
•
•
TRIM IS THE DIFFERENCE BETWEEN THE AFT DRAFT & THE FORE DRAFT. TRIM
COULD 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
L2
L1
ф
LBP IS THE LENGTH BETWEEN PERPENDICULAR
L1 DISTANCE FROM AFT B. TO MID SHIP ,CF
L2 DISTANCE FROM FORE B. TO MID SHIP,CF
ф MIDSHIP
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.
L
LBP
L2
DRAFT
FORE
ф
CF
L1
DRAFT
AFT
LONGITUDINAL STABILITY
TRIM
•
WHEN A LOAD IS ADDED ,THE G WILL 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.
GML
W
G’
B’
ф
G
B
LONGITUDINAL STABILITY
TRIM
• CENTRE OF FLOATATION
IS THE CENTRE WHERE THE LINES OF WATER
INTERSECTS . THE SHIP TRIM LONGITUDINALY AROUND THIS POINT. THE DRAFT
AT THIS POINT IS CONSTANT.
LBP
L2
L1
ф
NEW
DRAFT
FORE
CF
NEW
DRAFT
AFT
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 SHIP’S TRIM COMES FROM THE MOMENT IT MAKES.
TRIMMING MOMENT IS THE MOMENT TO CHANGE THE SHIP’S TRIM ,& IT IS THE
SUM OF THE W & DISTANCE OF W FROM CF.
trimming moment = _w * d
MEASURED IN TON METER
W
LBP
L2
L1
ф
NEW
DRAFT
FORE
CF
Fig.1
d
W
NEW
DRAFT
AFT
LONGITUDINAL STABILITY
TRIM
•
TRIMMING MOMENT = w * d MEASURED IN TON METER
W
MCTC : IS THE MOMENT THAT CHANGE THE TRIM BY 1 CM .
CHANGE OF TRIM IS THE TOTAL CHANGE IN THE SHIPS TRIM FROM THE RATIO
BETWEEN THE MOMENTS OCCURRED & THE MCTC.
MEASURED IN CM = TRIMMING MOMENT
MCTC
LBP
L2
L1
ф
NEW
DRAFT
FORE
CF
Fig.1
d
W
NEW
DRAFT
AFT
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
L2
L1
ф
CF
Fig.1
d
W
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
L2
L1
ф
NEW
DRAFT
FORE
CF
Fig.1
d
W
NEW
DRAFT
AFT
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
L2
L1
ф
NEW
DRAFT
FORE
CF
Fig.1
d
W
NEW
DRAFT
AFT