1. Principles of Ship’s Stability
PETRAS PIKSRYS

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

3. WHAY IS STABILITY IS SO IMPORTENT ?
IF THE SHIP LOST STABILITY WHAT WILL BE HAPPENED:
1. LOST OF MOBILE
2. LOST THE HUMANS LIFES 3. LOST THE SHIP
4. LOST THE CARGO
5. OIL POLLUTION

4. FUNDAMENTALS OF STABILITY
STABILITY is the tendency of vessel to rotate one way or the
other when forcibly inclined.
IMPORTENT !!
Ship’s stability can’t catch directly
Stability can define only by calculating

5. HOW CALCULATING SHIP”S STABILITY AND CARCO PLAN ?
1.By previous similar cargo plan.
2.By standard cargo plan according “STABILITY BOOKLET”
3.By standard cargo plan forms
4.By special cargo plan computer
5.By standard PC with special cargo plan program
6.By special or standard hand calculator

6. SHIP’S STABILITY CRITERIAS
THERE ARE TWO SHIP’S STABILITY CRITERIAS:
1 h>0 ship’s metacenter height always positive.
2 Zg < Zcritical
h = Zm – Zg
Zg defined by calculating
Zm define according hydrostatic curves
Zg critical define according special diagram.

7. SHIP’S STABILITY CALCULATING
SHIP’S STABILITY CALCULATING BY MOMENT FORMULAS.
MAIN OBJECT OF CALCULATING TO DEFINE SHIP’S STABILITY CRITERIAS:
GM=h METACENTER HEIGHT
Zg SHIP’S GRAVITY HEIGHT
MOMENT FORMULA:
D0Z0+P1Z1+P2Z2+…….+PnZn
Zg =
D0 + P1 +P2 + …….. + Pn

8. SHIP’S STABILITY CALCULATING
Zg critical CURVE
6.60
6.50
6.40
Zg critical
6.30
6.20
6.10
8000
10000
12000
14000
16000
18000
20000 D

9. WHO CALCULATING SHIP’S CARGO PLAN AND STABILITY?
1.CARGO OFFICER (ch.mate)
2.PORT CARGO OFFICER (supercargo)
3.SHIP’S MASTER

10. SHIP’S STABILITY

11. STABILITY
INITIAL STABILITY - The stability of a ship in the range from 0° to 7°/10° of inclination.
OVERALL STABILITY - A general measure of a ship's ability to resist capsizing in a given condition of loading.
DYNAMIC STABILITY - The work done in heeling a ship to a given angle of heel.

12. INITIAL SHIP’S STABILITY
Initial ship’s stability when ship inclinating from 7 till12 degrees. Ship’s underwater body did not change volume
V0=V1 V1 m L1 V0 G w L C1 W1 C

13. INITIAL METACENTRIC FORMULA
M=D lst
Qst m
lst=hsinQ h
M=D h sin Q
lst G D Vg C1 C

14. SHIP’S STABILITY CALCULATING
Initial stability calculating by ship’s stability triangle
Calculating formula lst= h sinQ
Overall stability calculating by hydrostatic ship’s body formula lf
Dynamic stability is the area under the static stability curve
Dynamic stability also potential energy available to return the ship to the upringing

15. STABILITY TRIANGLE m
lst =hsin Q h Q
l f
l st G Vg D C1 lf C

16. SHIP’S BADY FORM STABILITY ARMS lf
PHANTACORENS
SHIP’S BADY FORM STABILITY ARMS lf lf
2.8 80 90
2.4 70 60
1.6 50
ARMS lf 40
1.2 30
0.8 20
0.4 10
4000
6000
8000
10000
12000
16000
20000
14000
18000
DISPLACEMENT

17. METACENTRIC HEIGHT
Metacentric height GM is calculated by subtracting KG
From KM (GM=KM-KG), GM is a measure of the ship.s
stability. KM=h.
With initial stability(0 – 10 deg.) the metacenter does not
move, and Sine function is almost linear(a straight line).
Therefore, the size of the ship,s Righting Arm, GZ, is
directly prportional to the size of the ship’s Metacentric
Height, GM.
IMPORTENT !
Thus , GM is a good measure of the ship’s
initial stability.

18. METACENTRIC HEIGHT m h L W G a a C

19. MAIN STABILITY POINTS There are three main stability points:
m- metacenter is the end of hydrostatic force when ship listing.
G- centre of ship gravity
C- centre of ship underwater body.

20. SHIP’S STABILITY
STABILITY REFERENCE POINTS m h Zm G WO r Lo ZG a C Zc

21. MAIN STABILITY POINTS h Wo m Q LO a G C m metacenter
G center of gravity
C center of buoyancy m Q L1 h Q Wo LO a G W1 C C1

22. SHIP’S STABILITY
METACENTER m C0

23. SHIP’S STABILITY METACENTRIC HEIGHT FORMULAS h=r-a h=zm – zG
h=zc - ro - zG

24. METACENTRIC HEIGHT
METACENTRIC HEIGHT MEENS SHIP’S INITIAL STABILITY m h L W G r0 a C

25. Three states of static equilibrium
(a) Positive stability - m above G
(b) Neutral stability – m and G in
the same position
( c )Negative stability –m below G m G G m
h=O
h<O
h>O G m c b a

26. POSITIVE SHIP’S STABILITY
Positive ship’s stability when m above G
h>0 m L1 h W L G W1 C1 C

27. SHIP’S STABILITY CURVE
POSITIVE SHIP’S STABILITY L
l st
h>0 h
57, 3 Q Q

28. NEUTRAL SHIP’S STABILITY
Neutral ship’s stability when m and G in the same position
h=0
G m L W C C1

29. SHIP’S STABILITY
NEUTRAL SHIP’S STABILITY
h=0
lst Q

30. NEGATIVE SHIP’S STABILITY
Negative ship’s stability when m below G
h<0 L1 G h W L m C1 W1 C

31. NEGATIVE SHIP’S STABILITY
Mst
Qst
57.3 -h

32. STABILITY CONDITIONS
The positions of Gravity and the Metacenter will indicate the initial stability
of a ship.
Following damage, the ship will assume one of the following three stability
conditions:
1. POSITIVE STABILITY. The metacenter is located above
the ship’s center of gravity.
As the ship is inclined, Righting Arm are created which tend
to return the ship to it’s original, vertical position.
2. NEUTRAL STABILITY. The metacenter and the ship’s
center of gravity are in the same location. As the ship is inclined, there are no returing moment.
3. NEGATIVE STABILITY. The ship,s center of gravity is
above the metacenter.
As the ship is inclined, negative Righting Arms (called upsetting
arms) are created which tend to capsize the ship.

33. METACENTRIC FORMULA OVERALL h=Zm - ZG M M=( lf —lst)D m h lst G D C1W0 L0 Vg D C1 Zm ZG lf W1 C
M- UPSERTING MOMENT

34. METACENTRIC HIGHT h 57,3 Mst lst Q
METACENTRIC HIGHT IS FIRST DERIVATIVE SHIP”S STABILITY CURVE
Mst
lst h Q
57,3

35. METACENTER MOMENT IS UPSERTING MOMENT
METACENTER HEIGHT
Metacenter height GM is a determine of ship’s stability curve L1 m h L W G C1 W1 C
METACENTER MOMENT IS UPSERTING MOMENT
M= D h sin Q

36. DYNAMIC STABILITY W L

37. SHIP’S DYNAMIC STABILITY
DYMAMIC MOMENT M
M DYNAMIC MOMENT Q

38. SHIP’S STABILITY
STATIC MOMENT CURVE M Q

39. SHIP’S DYNAMIC STABILITY
MAXIMUM DYNAMIC ANGLE
Qdyn WHEN S1= S2 M S2 S1 Q
Q static
Q dyn
Q dyn max

40. SHIP’S DYNAMIC CURVE S=Mdyn Mdyn
SHIP’S DYNAMIC STABILITY CURVES APPLICATES IS EQUVALENT STATIC CURVES AREA
S=Mdyn
Mdyn S
Mdyn Q

41. DYNAMIC STABILITY
The dynamic stability is the area under the curve in metre-radians
Multiplated by the ship,s displacement in tonnes. It is areas under
the GZ
Curve which are required for checking stability criteria which
depending
Upon the ship,s data may be expressed in metre-degrees or
metre-radians.
The area unde GZ curve also the potential energy available to
return the
Ship to the upringht.
Principle of conservation of energy, the potential energy
in converted into
Rotation energy as the ship moves towards the upright.

42. DYNAMIC STABILITY
CURVE
Mst
Mst
Mdin Md Q Q
max

43. STABILITY ELEMENTS
THE LAW OF BUOYANCY
THE LAW OF GRAVITY
STABILITY REFERENCE POINTS
LINEAR MESURMENTS IN STABILITY
THE STABILITY TRIANGLE
RIGHTING MOMENT
STATIC STABILITY CURVE DYNAMIC STABILITY CURVE ROLLING PERIOD

44. Learning Objectives
Comprehend the concepts of hydrostatics, buoyancy, and Archimedes' principle
Comprehend static equilibrium of a floating vessel and the relationship of the centers of gravity and buoyancy to righting arms and stability
Comprehend and identify positive, negative and neutral conditions of stability
Comprehend the effects of movements of the centers of gravity and buoyancy on vessel stability
Know how ship's stability curves are derived and comprehend their use in determining stability condition

45. Definitions
Draft
Freeboard
Depth of hull
Reserve buoyancy
List / Trim

46. SHIP’S HULL MARKINGS
At XVIII hundred one Englishman called
PLIMSOL in Great Britan Parlament filds
for marcks on the hull to for Safe shipping.
Now thats marks called PLIMSOL MARKS.

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

48. FREE BOARD SHIP’S MAIN FREE BOARD MEENS SHIP’S RESERVE BUOYANCY DRAFT
SHIP’S MAIN DRAFT MEENS SHIP’S DISPLACEMENT

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

50. FREE BOARD MEENS RESERVE BUOYANCYTF
FREE BOARD F S WL W
WNA

51. DRAFT
MAIN DRAFT MEENS SHIP”S DISPLACEMENT W L
DRAFT

52. Buoyancy Archimedes' principle Calculations of displacement (W)
The effect of salt water and fresh water on displacement (relate to draft)
[1/35 vs 1/36]

53. Archimede’s principle
BOYAD
A body immersed (or floating) in water will
buoyed
ARCHIMEDE’S FORCE
By a force equal to the weight of the water
displaced.

54. THE LAWS OF BUOYANCY
Floatating objects posses the property of buoyancy.
A floatating body displaces a volume of water equal in
a body immersed (or floating) in water will be duoyed
up by a force equal to the weight of the water displaced
D=Vg D L W G C Vg

55. SHIP’S BUOYANCY
D=V*g L G W D
V*g C
ARCHIMEDES FORCE

56. PLIMSOL MARKS (Load lines)
Markings of minimum allowable freeboard for registred cargo-
Carryng ships.Located amidships on both the port and starboard
sides the ship.
Since the required minimum freeboard varies with water density
and severity of weather, different markings are used for:
- TF – Tropical Fresh Water
- F Fresh Water
- T Tropical Water (sea water)
- S Standard Summer
- W - Winter
- WNA-Winter North Atlantic TF F T S W
WNA

57. SHIP’S HULL MARKINGS Calculative Draft Marks
Used for determining displacement and other properties
of the ship for stability and damage control.
Those draft marks indicate the depth of the keel (baseline)
below the waterline.
TWO POSIBLE MARKING SYSTEMS:
1. Roman numerals in height
2. Arabic numerals in height

58. DRAFT IN FEETS
1 ft = m
XVII
XVI XV
XIV
XIII

59. DRAFT IN METRES
1 ft = m 44 42 40 38 36

60. SHIP’S HULL MARKINGS
Navigational Draft Marks
Ship’s operational drafts.
These draft marks include the depth of any projections below the keel of the ship.
Limiting Draft Marks
Limiting drafts are assigned to maintain reserve buoyancy (freeboard) prior to damage, and to prevent excessive hull stresses as a result of overloading.

61. DISPLACEMENT GRAVITY MOMENT
The weight of the volume of water that is displaced by the
underwater portion of the hull is equal to the
weight of the ships
GRAVITY
The force of gravity acts vertically downward through the ship’s center
Of gravity. The magnitude of the force depends on the ship’s total weight.
MOMENT
The endency of a force to produce a rotation about a pivot point.
This works like a torque wrench acting on a bolt.

62. DISPLACEMENT
D=DLS + DS + DC
D – Displacement
DLS – Weight light ship
DS - Weight supply
DC - Weight cargo

63. GRAVITY
THE FORCE OF GRAVITY ACTS VERTICALY DOWNWARD THROUGHT THE SHIP”S CENTER OF GRAVITY W G L
DL+DC+DS D=

64. SHIP’S STABILITY
METACENTER MOMENT =UPSERTING MOMENT
M = D h sin O

65. RIGHTING MOMENT
THE TENDENY OF A FORCE TO PRODUCE A ROTATION ABOUT A PIVOT POINT m
M = D h sinQ h Vg G D C1 C0

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

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

68. DEFINITIONS
Couple. Since the forces of buoyancy and gravity are equal and act
along parallel lines, but in opposite directions, a rotation is developed.
Righting arm. The distance between the forces of buoyancy and
gravity is know as the ship’s righting arm.
Righting moment. The righting moment is equal to the ship’s
Righting arm multiplied by the ship’s displacement.
Metacentric height. The distance between center of gravity G and
Metacener M .

69. - G does not change position as heeling angle
The development of the static stability curve from the cross curves of stability
Foctors involed:
- G does not change position as heeling angle
changes
- C is always at the geometric center of the volume
of the underwater hull
- the shape of the underwater hull changes as
heeling angle changes

70. SHIP’S STABILITY CURVE
Using curves,find
(a) Maximum rigting arm (GZ) GZ=h
(b) Angle of heel where maximum GZ arm ocurs
l static maximum
(c) Range of critical stability Q critical
SHIP’S STABILITY CURVE

71. SHIP’S STABILITY STABILITY CURVES ELEMENTS h Q Q critical lst
l static max h Q
57.3
Q critical

72. STATIC STABILITY CURVE
When a ship is inclined through all angles of heel,and the
righting arm for each angle is measured, the statical stability curve is produced. This curve is a “snapshot”of the ship’s stability at that particular loading condition.Much information can be obtained from this curve, including:
Range of Stability: This ship will generate Righting Arms when inclined from 0 deg. Till to approximately 74 dg.
Maximum Righting Arm: The angle of inclination where the maximum Righting Arm occurs
Danger Angle:One half the angle of the maximum Righting Arms.

73. DRAFT DIAGRAM AND FUNCTIONS OF FORM
The Draft Diagram is a nomogram located in
Section II(a) of the Damage Control Book.
It is used for determining the ship’s displacement, as well as other
properties of the ship, including:
- Moment to Trim One Inch (MT1);
- Tons per Inch Immersion (TPI);
- Height of Metacenter (KM);
- Longitudinal Center of Flotation (LCF)
- Longitudinal Center of Buoyancy(LCB)
-Displacement (D)
-VOLUME V m
-Moment, diferenting per 1 cm
-Weight, drafting per 1 cm

74. DRAFT NOMOGRAM Tm Dt Vm M t/cm P t/cm 8.2 18000 17900 19900 26.5 7.8
17000
16860
18800 26
7.2
16000
15845
17600
25.5
6.8
15000
14840
16600 25
6.4
14000
13840
15500
24.5
6.0
13000
12820 24
5.6
12000
11820
14600
23.5
5.2
11000
10820
14400 23
4.8
10000
9820
14200
22.5
4.4
9000
8820 22 Tm Dt Vm 3
M t/cm
P t/cm

75. HYDROSTATIC CURVES
SHIP’S FLOATING BODY FUNCTIONS CAN CALCULATING BY HYDROSTATIC CURVES. THIS CURVES IS FUNCTIONS FLOATING SHIP’S BODY STABILITY AND UNDERSEA SHIP’S BODY CAPITICY.
ARGUMENT FOR CALCULATING IS SHIP’S DRAFT
FUNCTIONS FOR CALCULATING:
a) DISPLACEMENT D
b) VOLUME V
c) FLOATING CENTER Xf
d) BOYAD CENTER XC Zc
e METACENTER RADIUS r
f) SQUERE OF WATERLINE S

76. HYDROSTATIC CURVES SHIP’S FLOATING BODY FUNCTION CURVES V Zc r Xf D S
DRAFT V Zc r Xf D S
FUNCTIONS

77. COUPLE m
M=D h sin Q h Q
l st G Vg D C1 C

78. PLIMSOL DISC TF T F S W
WNA

79. LIST Q L1 Lo Q WO W1

80. ROLLING PERIOD
C B T=
SHIP”S STABILITY AND ROLLING PERIOD h L W

81. B – the ship’s beam to outside of hull.
ROLLING PERIOD
The rolling period of the ship’s dependenced from ship’s stability. The formula
Between ship,s stability and rolling :
T = c*B/sqr GM
In this formula:
T – rollinperiod in sec.
c - constanta
B – the ship’s beam to outside of hull.
Note: the constanta c dependenced from ship’s displacements.
There are the followings meanings:
c=0.88 – when ship is empty or ballast;
c= when the ship has on board amout 20 %
c=0.75 – when liquids on board 10%
c=0.73 – when all liquids on board amout 5%
HOWEVER, for all lagers ships Lloyd’s Register of shipping and the 1991 HMSO
Code of Practice for Ro-Ro ships use c= 0.7

82. SHIP’S STABILITY VARIATIONS
LOADING CARGO m0 h0 G0 C0
STABILITY REFERENCES POINTS BEFORE LOADING

83. SHIP’S STABILITY VARIATIONS
h0 < h1
LOADING CARGO IN HOLD m1 m0 h1 h0 G0 G1 C1 C0 p
STABILITY REFERENCES POINTS AFTER LOADING

84. SHIP’S STABILITY VARIATIONS
h0 >h1
LOADING CARGO AT DECK m1 P2 P1 m0 h1 h0 G1 G0 C1 C0
STABILITY REFERENCES POINTS AFTER LOADING

85. SHIP’S STABILITY VARIATIONS
MOVING CARGO m0 h0 G0 C0
STABILITY REFERENCES POINTS BEFORE MOVING

86. SHIP’S STABILITY VARIATIONS
MOVING CARGO P2 m0 P1 h0 G0 C0
STABILITY REFERENCES POINTS BEFORE MOVING DOWN

87. SHIP’S STABILITY VARIATIONS
h1 > h0
MOVING CARGO m0 h0 h1 G0 G1 C0 P2 P1
STABILITY REFERENCES POINTS AFTER MOVING DOWN

88. SHIP’S STABILITY VARIATIONS
MOVING CARGO m0 h0 G0 C0 P2 P1
STABILITY REFERENCES POINTS BEFORE MOVING UPWARD

89. SHIP’S STABILITY VARIATIONS
h0 > h1
MOVING CARGO P2 m0 P1 h1 h0 G1 G0 C0
STABILITY REFERENCES POINTS AFTER MOVING UPVARD

90. SHIP’S STABILITY VARIATIONS
LOADING CARGO m h0 h1 G0 G1 L0 W0 C0

91. SHIP’S STABILITY VARIATIONS
FREE LIQUID AREA G0 L0 W0 C0 P0

92. SHIP’S STABILITY VARIATIONS
M Moment liquid
SHIP’S STABILITY VARIATIONS
M Moment upserting
FREE LIQUID AREA m L1 G0 Q L0 W0 C1 C0 W1 P1 P1

93. SHIP’S STABILITY VARIATIONSM1
FREE LIQUID AREA Y1 Q1 M2 P1 Y2 P2
Q2>Q1
M2>M1 Q2

94. SHIP’S STABILITY VARIATIONS
Mcargo
SHIP’S STABILITY VARIATIONS
HANGING CARGO Q lz W0 L1 P L0 W1
Mcargo= Pcargo lz sin Q

95. TRIM
Trim means different between draft fore TF and draft aft TAF W1 W L
NOTE Ship”s trim is one element of ship”s stability and buoyancy
TAF L1 TF

96. SHIP’S TRIM DIAGRAM TAf Tf m 9 8 D=19000t 7 6 5 4 3 2 1 2 3 4 5 6 7 8
Xc=28m 7
18000t
30m 6
32m
16000t
17000t
34m
15000t 5
36m
14000t
38m 4
40m
10000t
42m 3
9000t
44m
8000t
7000t
46m 2
48m Tf 1 2 3 4 5 6 7 8 9 m

97. SHIP’S TRIM DIAGRAM Dt 4000 Tf=6m TAf=6.4m 3600 5.8m 6.0m 5.4m 3200
2800
5.2m
4.8m
4.6m
2400
4.4m
4.4m
1600
3.8m
3.2m
4.0m
3.0m
1200
3.2m
3.6m 3 -5 -4 -3 -2 -1 1 2
Xc m

98. TRIM W1 lx TAF L1 P TF SHIP’S TRIM BEFORE SHIFTING CARGO
SHIP’S STABILITY VARIATIONS
TRIM
Trim means different between draft fore TF and draft aft TAF W1 W L lx
NOTE Ship”s trim is one element of ship”s stability and buoyancy
TAF L1 P TF
SHIP’S TRIM BEFORE SHIFTING CARGO
Mdif
D H

99. TRIM W1 TAF0 P P L1 TAF1 TF0 TF1 L SHIP’S TRIM AFTER SHIFTING CARGO
SHIP’S STABILITY VARIATIONS
TRIM
Trim means different between draft fore TF and draft aft TAF
P lx
d = L
D H W1 W L
NOTE Ship”s trim is one element of ship”s stability and buoyancy
TAF0 P P L1
TAF1 d lx
TF0
TF1 L
SHIP’S TRIM AFTER SHIFTING CARGO

100. LIST Q L1 Lo Q WO W1

101. LIST Lo WO P SHIP’S STABILITY VARIATIONS
SHIP’S LIST BEFORE SHIFTING CARGO

102. LIST WO Lo SHIP’S STABILITY VARIATIONS ly P P L1 Q W1 P ly tg Q = D h
SHIP’S LIST AFTER SHIFTING CARGO