1. STABILITY
BASIC COURSE

2. CHAPTER 3
A-DENSITY
B-RELATIVE DENSITY

3. A-DENSITY
• DENSITY :
THE MASS PER UNIT VOLUME MEASURED IN KG/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 )

4. 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

5. CHAPTER 4
LAW OF FLOATATION

6. 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 = 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 VOLUME
DISPLACED BY THE PART UNDER WATER
( L * B * DRAFT )SO
SHIPS MASS = WATER DISPLACED MASS
DENSITY OF SHIP * DEPTH = DENSITY OF WATER * DRAFT

7. LAW OF FLOATATIONTHE 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
W
G
₀

8. 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
DRAFT ₀

9. LAW OF FLOATATION
W
KG = ½ DEPTH
DEPTH
G
B
DRAFT K
KB = ½ DRAFT
B

10. 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 .

11. 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 WATER
OR
RESERVE BOUYANCY = AREA OF THE SHIP - AREA UNDER WATER

12. EFFECT OF DENSITY ON SHIP’S
VOLUME & DISPLACEMENT
A- BOX SHAPE VESSELS
B- SHIP SHAPE VESSELS
CHAPTER 5

13. A-BOX SHAPED VESSELES
1-EFFECT OF DENSITY ON SHIP’S VOLUME
2-EFFECT OF DENSITY ON SHIP’DISPLACEMENT

14. 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
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

15. 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 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 ONLY PARAMETER
THAT CHANGES IS THE DRAFT ,THERFORE THE VOLUME CHANGES ASWELL

16. A-BOX SHAPED SHIPS
1-EFFECT OF DENSITY ON VOLUME

17. 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

18. 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 )

19. A-BOX SHAPED SHIPS
2-EFFECT OF DENSITY ON DISPLACEMENT

20. 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)

21. 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 NEW MASS
------------------------- = ----------------------
OLD DENSITY NEW DENSITY

22. B- SHIP SHAPED VESSELS
EFFECT OF DENSITY ON SHIP’S VOLUME &
DISPLACEMENT

23. EFFECT OF DENSITY ON VOLUME & DISPLACEMENT
• INORDER TO UNDER STAND THE EFFECT WE SHOULD
VERY WELL UNDERSTAND THE PLYMSOL MARK ( DRAFT
MEASURES)
FREE BOARD
(RESERVE BOUYANCY )
54
WNA
Winter
Summer
FWA
Fresh
Tropical F
Tropical 230mm
300mm
540mm

24. 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

25. 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

26. 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 )

27. 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

28. STATIC STABILITY
CHAPTER 6

29. STATIC STABILITY
HEELING ,
IS THE ANGLE CREATED BY THE SHIP WHEN HEELED TO ONE SIDE DUE TO EXTERNAL FORCES
(WIND,WAVES)
LIST,
IS THE ANGLE CREATED BY THE SHIP WHEN HEELED 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 )

30. STATIC STABILITY
K
G
K
M
G
M
K
B B B

31. STATIC STABILITY
KM = KG + GM
KM = KB + BM
KG = KB + BG
KG = KM - GM
GM = KM - KG
KB = ½ DRAFT , KG = ½ DEPTH
CENTRE OF BOUYANCY
ALWAYS MOVES TO THE HEELED SIDE TO BE CENTERED IN ½ THE UNDER WATER
VOLUME

32. 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•
•
•
•

33. 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
M
B’
K
W
L
G
B
W
•

34. 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 CONDITION . THE STATICAL RIGHTING MOMENT IS THE SUM OF THE RIGHTING
LEVER & THE SHIPS DISPLACEMENT.
THE RIGHTENING LEVER IS REPRESENTED BY GZ.
THE GZ THAT APPEARS , STARTS FROM THE G POINT TO THE LINE OF BOUANCY MAKING A
RIGHT ANGLE.
STATICAL RIGHTING MOMENT = RIGHTING LEVER * DISPLACEMENT
RM ( TON METER) = GZ (mtrs) * ∆ ( tons )

35. 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

36. 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 = - GZ * DISPLACEMENT
- RM = - GZ * ∆

37. STATIC STABILITY
UNSTABLE SHIP
UNSTABLE SHIP
W
K
B
M
G
B
W
K
B B’
M
GZ
B
B
W
GZ
•
•
•
•
•
•
•
STATICAL CAPSIZING MOMENT = - GZ * DISPLACEMENT
A COUPLING IS SET & INCREASES THE SHIPS HEEL OR LIST

38. 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.
THE
K
B
M G
B
W
B B’
K
G M
W
B
B
W
•
• •

39. 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
K
G
M

40. 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
K
G
M

41. 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)

42. 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.

43. STATIC STABILITY
ANGLE OF LOLL
M
GZ
B
B’
K
B
B’
M G
B B’
G Z
M
B
W
B
W
B
W
CAPSIZING
MOMENT
WIND
WIND
WIND
RIGHTENING MOMENT
Fig.1 Fig.2
Fig. 3
LOLL
•
•
•
•
•
•
•
•
•
• •
•

44. STATIC STABILITY
CORRECTING ANGLE OF
LOLLINORDER TO CORRECT < OF LOLL WE MUST LOWER THE G BELOW M ,
PUTTING INTO CONSIDERATION THE SEQUENCE.
1. FILLING THE ½ FULL BALLAST TANKS ( TO REMOVE FREE SURFACE)
2. LOWERING DOWN ANY UPPER LOADS ( CRANES , TOPSIDES TODOUBLE BOTTOM TANKS)
3. FILLING THE D.B TANKS IN THE HEELED SIDE
4. 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.

45. STATIC STABILITY
CORRECTING ANGLE OF
LOLLIF 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.

46. FINAL KG
CHAPTER

47. 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
K K
G G
G’
g
g
G’
Fig. 1 Fig.2

48. 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

49. 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 )
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
w/tons Kg/m MOMENT/ ton m
100 10 1000
200 5.0 1000
Total w Total M
300 2000
6.6m
1.4m

50. FINAL KG
• GG’IS THE MOVE OF G TO G’ DURING LOAD/DISCH
LEADING 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 G’M
INITIAL GM

51. GZ CURVES
CHAPTER

52. 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
Ѳ
heel
GZ = GM * SIN Ѳ
B
M
K
G
B’
Z
G Z
M B’
•
•
•

53. 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.
3.9m
57.3
Vanishing angle
91 ⁰
Max GZ
Ѳ 40⁰
Max GZ
ARCHI LINEGZ
10 20 30 40 50 60 70 80 90
GM 1.1 m
4
3
2
1
0

54. GZ CURVES
STABLE SHIP
• MAX GZ = 4.0 m AT Ѳ 39.0⁰ RANGE OF STABILITY = 0—90 ⁰
• INITIAL GM = 1.3 m AT Ѳ 57.3⁰ VANISHING ANGLE = 90⁰
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

55. 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
57,32510 20 30 40 50 60 70 80 90

56. GZ CURVES
UNSTABLE SHIP
GZ RANGE OF STABILITY 17 ⁰--- 83⁰ Ѳ LOLL 17⁰
MAX GZ 3.8m at Ѳ 43⁰ VANISHING Ѳ 83⁰
MAX GZ AT 43⁰
Ѳ LOLL
17⁰
43⁰
UNSTABLE SHIP –VE GZ CURVE
83⁰
RANGE OF UNSTABILITY 0⁰ --- 17⁰
< LOLL
GZ
10 20 30 40 50 60 70 80 90
0
-1
-2
1
2
3
4.0

57. GZ CURVES
UNSTABLE SHIP
4_
3_
2_
1_
0 | | | | | | | | | |
-1
UNSTABLE SHIP -VE GZ
57.3
-2
-3
Ѳ LOLL
22⁰
GM – 3m
RANGE OF UNSTABILITY 0⁰--- 22⁰
RANGE OF STABILITY 22⁰ -- 92⁰
INITIAL GM - 3 m
GZ
10 20 30 40 50 60 70 80 90 100

58. FREE SURFACE
CHAPTER 7

59. 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.

60. 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
G’Z < GZ NEW MOMENY< OLD MOMENT
NEW G1M < OLD GM GG1 = LOSS IN GM
M
G1
Z1
G
Z
B
B’g
g
G’

61. 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

62. FREE SURFACE
• SUMMARY
1. FREE SURFACE COMES FROM ½ FULL TANKS
2. 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

63. TRANSVERSE STABILITY
LIST
CHAPTER

64. 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)

65. TRANSVERSE STABILITY
LIST
• The IDEA IS EQUIVILANT FROM THE point of VIEW OF A SIMPLE BALANCE.
2OO
100
1OO
3OO
3OO
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

66. TRANSVERSE STABILITY
LIST
• The SHIP LIST IS VERY SIMILLAR TO THE LAST EXAMPLE CONCEPT.
STBPORT
d d
dd
d d
d
d
d 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

67. TRANSVERSE STABILITY
LIST• A DEEPER VIEW TOWARD THE EFFECT OVER THE SHIP’S STBILITY “GM”
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’ ,
TAN Ѳ = GG ‘
GM
Ѳ IS THE LISTING ANGLE
K
G G’
M
Ѳ
B
B’
W
B
G G’
M
Ѳ

68. TRANSVERSE STABILITY
LIST
w D ( gg’)
Distance from centre
line
Moment
port
Moment
Strb
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 6750 8000

69. 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 Ѳ = GG’ 0.781 = 8⁰ strb
GM 5.50
G G’
M
0.781
5.5
8⁰

70. LONGITUDINAL STABILITY
TRIM
CHAPTER

71. 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
ф
L1L2
LBP IS THE LENGTH BETWEEN PERPENDICULAR ф MIDSHIP
L1 DISTANCE FROM AFT B. TO MID SHIP ,CF
L2 DISTANCE FROM FORE B. TO MID SHIP,CF

72. 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
ф L1L2
DRAFT
FORE
DRAFT
AFTCF
L

73. 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.
ф
W
GG’
BB’
GML

74. 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
ф
L1L2
CF
NEW
DRAFT
AFTNEW
DRAFT
FORE

75. 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
ф
L1L2
CF
NEW
DRAFT
AFTNEW
DRAFT
FORE
W
Fig.1
d

76. 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
ф
L1L2
CF
NEW
DRAFT
AFTNEW
DRAFT
FORE
W
Fig.1
d

77. 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
ф L1L2
CF
W
Fig.1
d

78. 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
ф
L1L2
CF
NEW
DRAFT
AFTNEW
DRAFT
FORE
W
Fig.1
d

79. 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 TPCL
ф
L1L2
CF
NEW
DRAFT
AFTNEW
DRAFT
FORE
W
Fig.1
d