This document provides an introduction to ship stability, including definitions of key terms like stability, buoyancy, and displacement. It discusses stability reference points like the center of buoyancy, gravity, and metacenter. Conditions of stability like positive, neutral, and negative are defined. The stability triangle and how righting arm is calculated is explained. Other topics covered include stability curves, hull markings, draft diagrams, and using a model to demonstrate concepts.

1. Lesson-1
Introduction to Stability
CL
M
G
B
K
BM
KM
DISPLACEMENT
B
G

2. CLASS TOPICS
1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings
7. Draft Diagram and Cross Curves
8. Model

3. Definitions :
• Stability
• Initial Stability
• Overall Stability
• Dynamic Stability

4. STABILITY - THE TENDENCY OF A SHIP TO
ROTATE ONE WAY OR THE OTHER (TO RIGHT
ITSELF OR OVERTURN)
INITIAL STABILITY - THE STABILITY OF A
SHIP IN THE RANGE FROM 0° TO 7°/10°
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

5. LAWS OF BUOYANCY
• A FLOATING OBJECT HAS THE PROPERTY OF
BUOYANCY
• A FLOATING BODY DISPLACES A VOLUME
OF WATER EQUAL IN WEIGHT TO THE
WEIGHT OF THE BODY.

6. LAWS OF BUOYANCY
• A FLOATING OBJECT HAS THE PROPERTY
OF BUOYANCY
• A FLOATING BODY DISPLACES A VOLUME
OF WATER EQUAL IN WEIGHT TO THE
WEIGHT OF THE BODY.
• A BODY IMMERSED (OR FLOATING) IN
WATER WILL BE BUOYED UP BY A FORCE
EQUAL TO THE WEIGHT OF THE WATER
DISPLACED.

7. DISPLACEMENT
• THE WEIGHT OF THE VOLUME OF WATER
THAT THE SHIP'S HULL IS DISPLACING
• UNITS OF WEIGHT
LONG TON = 2240 LBS = 1016 KG
SHORT TON = 2000 LBS = 907.184 KG
METRIC TON = 2204.72 LBS = 1000 KG

8. DISPLACEMENT
00
G
DISPLACEMENT

9. DISPLACEMENT
04
G
B
DISPLACEMENT

10. DISPLACEMENT
09
G
B
DISPLACEMENT

11. DISPLACEMENT
16
G
B
DISPLACEMENT

12. DISPLACEMENT
20
G
B
DISPLACEMENT

13. FORCE: A PUSH OR A PULL. IT TENDS TO
PRODUCE MOTION OR A CHANGE
IN MOTION.
UNITS: TONS, POUNDS, ETC.
PARALLEL FORCES MAY BE COMBINED INTO
ONE FORCE EQUAL TO THE SUM OF ALL
FORCES ACTING IN THE SAME DIRECTION AND
SO LOCATED TO PRODUCE THE SAME EFFECT.
5T
5T
5T
15T

14. WEIGHT : GRAVITATIONAL FORCE.
DIRECTION TOWARD CENTER
OF EARTH
UNITS : TONS, POUNDS, etc
MOMENT: THE TENDENCY OF A FORCE TO
PRODUCE ROTATION ABOUT AN
AXIS
MOMENT = F x d
a
d
F

15. VOLUME = NUMBER OF CUBIC UNITS
IN AN OBJECT
UNITS: CUBIC FEET
CUBIC INCHES
CUBIC METRES
V = L x B x D
6 M
V = 30 M x 20 M x 6 M
V = 3600 M3

16. SW = 0.97560976 M3/TON
FW = 1.000 M3/TON
SPECIFIC VOLUME = VOLUME PER
UNIT WEIGHT
UNITS: METRE CUBIC PER TON
6 M
V = 3600 M3
WT = VOLUME
SP.VOL
WT = 3600 M3 X 1.025 T/M3
WT = 3698,99 TONS
WT = 3600 M3 / 0.97560977 M3/T

17. CLASS TOPICS
1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings
7. Draft Diagram and Cross Curves
8. Model

18. 2. Stability Reference Points
• Metacentre
• Gravity
• Buoyancy
• Keel

19. STABILITY REFERENCE POINTS
CL
M
G
B
K
etacenter
ravity
uoyancy
eel

20. STABILITY REFERENCE POINTS
CL
other
M
oose
G
eats
B
ids
K

21. THE CENTER OF
BUOYANCY

22. B
WATERLINE
RESERVE BUOYANCY
B
THE CENTER OF
BUOYANCY
B1

23. WATERLINE
B
RESERVE BUOYANCY
RESERVE BUOYANCY, FREEBOARD, DRAFT
AND DEPTH OF HULL
DRAFT
FREEBOARD
DEPTH

24. CENTER OF BUOYANCY
B
WL
WL
B
WL
B
WL
B
WL
B

25. CENTER OF BUOYANCY
B
B
B
B
B
B
B
B
B

26. THE CENTER OF
GRAVITY

27. CENTER OF GRAVITY
• POINT AT WHICH ALL WEIGHTS COULD
BE CONCENTRATED.
• CENTER OF GRAVITY OF A SYSTEM OF
WEIGHTS IS FOUND BY TAKING
MOMENTS ABOUT AN ASSUMED CENTER
OF GRAVITY, MOMENTS ARE SUMMED
AND DIVIDED BY THE TOTAL WEIGHT
OF THE SYSTEM.

28. G
G1
KGo
KG1
THE CENTER OF
GRAVITY
G
G1
KGo
KG1

29. MOVEMENTS IN THE CENTER
OF GRAVITY
• G MOVES TOWARDS A WEIGHT ADDITION
• G MOVES AWAY FROM A WEIGHT REMOVAL
• G MOVES IN THE DIRECTION OF A WEIGHT
SHIFT

30. MOVEMENTS IN THE
CENTER OF GRAVITY
• G MOVES
TOWARDS
A WEIGHT
ADDITION
G
G1
KGo
KG1

31. G
KGo
G1
KG1

32. MOVEMENTS IN THE
CENTER OF GRAVITY
G MOVES AWAY FROM
A WEIGHT REMOVAL
G
G1
KGo
KG1

33. G
G
G
G
G
G
G1
KG1
KGo
G

34. MOVEMENTS IN THE
CENTER OF GRAVITY
G MOVES IN THE DIRECTION OF
A WEIGHT SHIFT
G G

35. G2
G

36. THE METACENTER

37. THE
METACENTER
B
B20
B45
M
M20
M45
M70
B70
METACENTER
M
B
B1 B2

38. METACENTER
B
BB
B
B
B
B
BB

39. METACENTER
B SHIFTS
M

40. MOVEMENTS OF THE
METACENTER
THE METACENTER WILL CHANGE
POSITIONS IN THE VERTICAL PLANE WHEN
THE SHIP'S DISPLACEMENT CHANGES
THE METACENTER MOVES LAW THESE
TWO RULES:
1. WHEN B MOVES UP M MOVES DOWN.
2. WHEN B MOVES DOWN M MOVES UP.

41. M
G
B
M
G
B
G
M
B
M1
B1
G
M
B
M1
B1
G
M
B
M1
B1
G
M
B
M1
B1
MOVEMENT OF
THE METACENTRE

42. CL
B
M
0o
-7/10o MOVEMENT OF
THE METACENTRE

43. B B20
M
M20
MOVEMENT OF
THE METACENTRE

44. M
M20
M45
B
B20 B45
MOVEMENT OF
THE METACENTRE

45. B
B20
B45
M
M20
M45
M70
B70
MOVEMENT OF
THE METACENTRE

46. CL
M20
M45
M70
M90
B
B20
B45
B70
B90
M
MOVEMENT OF
THE METACENTRE

47. MOVEMENTS OF THE
METACENTER
THE METACENTER WILL CHANGE
POSITIONS IN THE VERTICAL PLANE WHEN
THE SHIP'S DISPLACEMENT CHANGES
THE METACENTER MOVES LAW THESE
TWO RULES:
1. WHEN B MOVES UP M MOVES DOWN.
2. WHEN B MOVES DOWN M MOVES UP.

48. G
B
G
M
B
M1
B1
MOVEMENT OF
THE METACENTRE
G
WHEN B MOVES UP M MOVES DOWN.

49. GM
KG
CL
K
M
G
B
BM
KM
LINEAR MEASUREMENTS IN
STABILITY
KB

50. CLASS TOPICS
1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings
7. Draft Diagram and Cross Curves
8. Model

51. 3. Stability Triangle
M
G Z

52. M
G Z
THE STABILITY
TRIANGLE
CL
K
B
G
M

53. CL
K
B
G
M
M
G
B
K
B1
M
G
B
K
B1
M
G
B
K
B1
K
B
G
M
B1
Z
THE STABILITY TRIANGLE

54. M
G Z
Where :
opposite = GZ
hypotenuse = GM
Sin q = GZ / GM
GZ = GM x Sin q
Growth of GZ a GM
Sin q = opp / hyp

55. CL
K
B
G
M
G1

56. G
M
Z
G1 Z1
AS GM DECREASES
RIGHTING ARM
ALSO DECREASES
Growth of GZ α GM

57. INITIAL
STABILITY
G
B
M
0 - 7°
CL

58. M
Z
G
B B1
CL
OVERALL
STABILITY
RM = GZ x Wf

59. CLASS TOPICS
1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings
7. Draft Diagram and Cross Curves
8. Model

60. G
B1
M
Z
G
B1
M
B
G
B1
M
B
THE THREE CONDITIONS
OF STABILITY
POSITIVE
NEUTRAL
NEGATIVE

61. CL
K
B
G
M
POSITIVE STABILITY

62. K
B
G
M
B1
Z
POSITIVE STABILITY

63. CL
K
B
G
M
NEUTRAL STABILITY

64. K
B
B1
NEUTRAL STABILITY
G
M

65. CL
K
B
G
M
NEGATIVE STABILITY

66. K
B
G
M
B1
NEGATIVE STABILITY

67. CLASS TOPICS
1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings
7. Draft Diagram and Cross Curves
8. Model

68. RIGHTING
ARMS
(FT)
ANGLE OF HEEL (DEGREES)
90
60
30
0 10 20 40 50 70 80
20°
G
B
Z
40°
G
B
Z
60°
G
B
Z
GZ = 1.4 FT GZ = 2.0 FT GZ = 1 FT
RIGHTING ARM CURVE

69. RIGHTING
ARMS
(FT)
ANGLE OF HEEL (DEGREES)
90
60
30
0 10 20 40 50 70 80
20°
G
B
Z
40°
G
B
Z
60°
G
B
Z
GZ = 1.4 FT GZ = 2.0 FT GZ = 1 FT
MAXIMUM RIGHTING
ARM
ANGLE OF
MAXIMUM
RIGHTING
ARM
DANGER
ANGLE
MAXIMUM
RANGE OF
STABILITY

70. CLASS TOPICS
1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings
7. Draft Diagram and Cross Curves
8. Model

71. DWL
BL
LONGITUDINAL CROSS SECTION
FP
AP MP
LBP
20
9
8
30
9
8
7
20
9
8
30
9
8
7
26
5
4
PROJ
CALCULATIVE NAVIGATIONAL
LIMITING

72. CLASS TOPICS
1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings
7. Draft Diagram and Cross Curves
8. Model

73. DRAFT DIAGRAM AND FUNCTIONS OF FORM
17
16
15
14
13
12
11
800
4000
3500
3000
2550
750
700
650
600
550
AFTER
DRAFT
MARKS
(FT)
MOMENT TO
ALTER TRIM
ONE INCH
(FOOT-TONS) DISPLACEMENT
(TONS)
22.2
22.3
22.4
22.5
22.6
22.7
22.8
TRANSERSE
METACENTER
ABOVE BOTTOM
OF KEEL
(FT)
28
29
30
31
32
33
5
4
3
2
1
1
2
3
4
5
11
12
13
14
15
16
17
TONS
PER
INCH
(TONS/IN)
LONGITUDINAL
CENTER OF
BUOYANCY
(FEET)
FORWARD
DRAFT
MARKS
(FT)
CURVE OF CENTER OF FLOTATION
30 20 10
Length Between Draft Marks 397' 0"
DRAFT FWD = 14 FT 6 IN
DRAFT AFT = 16 FT 3 IN
Wo = 3850 TONS
KM =
TPI =
LCB =
LCF =
MT1" = 778 FT-TONS/IN
22.28 FT
32.7 TONS/IN
3.5 FT AFT
24 FT AFT

74. FFG 7
CROSS CURVES OF STABILITY
CENTER OF GRAVITY ASSUMED
19.0 FT ABOVE THE BASELINE
DISPLACEMENT (TONS)
RIGHTING
ARMS
(FT)
3000 3500 4000 4500
40
30
20
15
10
60
55
45
50
3.0
2.5
2.0
1.5
1.0
0.5
10o =
15o =
20o =
30o =
40o =
45o =
50o =
55o =
60o =
.55 FT
.85 FT
1.1 FT
1.73 FT
2.35 FT
2.55 FT
2.6 FT
2.5 FT
2.3 FT

75. 0
1
2
3
4
5
STATICAL STABILITY CURVE PLOTTING SHEET
RIGHTING
ARMS
(FT)
10o =
15o =
20o =
30o =
40o =
45o =
50o =
55o =
60o =
.55 FT
.85 FT
1.1 FT
1.73 FT
2.35 FT
2.55 FT
2.6 FT
2.5 FT
2.3 FT
X
X
X
X
X
X
X X X
X
10 20 30 40 50 57.3 60 70 80 90
ANGLE OF INCLINATION - DEGREES