1. Introduction to Stability
Lesson-1
Introduction to Stability CL M G B K BM KM
DISPLACEMENT T O N S W E I G H B

2. CLASS TOPICS Definitions Stability Reference Points Stability Triangle
Conditions of Stability
Stability Curve
Ship’s Hull Markings
Draft Diagram and Cross Curves
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 = KG SHORT TON = 2000 LBS = KG METRIC TON = LBS = 1000 KG

8. DISPLACEMENT
DISPLACEMENT 00 G

9. DISPLACEMENT
DISPLACEMENT 04 G B

10. DISPLACEMENT
DISPLACEMENT 09 G B

11. DISPLACEMENT G B
DISPLACEMENT 16

12. DISPLACEMENT G B
DISPLACEMENT 20

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
15T 5T

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

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

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

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 POINTSM
etacenter G
ravity B
uoyancy K
eel CL

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

21. THE CENTER OF BUOYANCY

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

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

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

25. CENTER OF BUOYANCY 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. G1
KG1
KGo G G G G G G G

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

35. G G2

36. THE METACENTER

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

38. METACENTER B B B B B B B B B

39. METACENTER M
B SHIFTS

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

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

43. MOVEMENT OF
THE METACENTRE
M20 M B
B20 CL

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

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

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

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

49. LINEAR MEASUREMENTS IN STABILITYCL K M G B GM BM KM KG 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. THE STABILITY TRIANGLEM G Z CL K B G M CL K B G M

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

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

55. G1 M G B K CL

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

57. INITIAL STABILITY G B M
0 - 7° CL

58. OVERALL STABILITY M Z G B B1 CL
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. THE THREE CONDITIONS OF STABILITYM
THE THREE CONDITIONS OF STABILITY G Z B1
POSITIVE G M B B1
NEUTRAL G M B B1
NEGATIVE

61. POSITIVE STABILITY M G B K CL

62. POSITIVE STABILITY M Z G B B1 K CL

63. NEUTRAL STABILITY G M B K CL

64. NEUTRAL STABILITY G M B B1 K CL

65. NEGATIVE STABILITY G M B K CL

66. NEGATIVE STABILITY G M B B1 K CL

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 ARM CURVE RIGHTING ARMS (FT) 10 20 30 40 50 60 70 80 9010 20 30 40 50 60 70 80 90
ANGLE OF HEEL (DEGREES) WL
60° G B Z WL
40° G B Z WL
20° G B Z
GZ = 1.4 FT
GZ = 2.0 FT
GZ = 1 FT

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

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. LONGITUDINAL CROSS SECTION
CALCULATIVE
LIMITING
NAVIGATIONAL MP AP FP
DWL BL
PROJ
LBP

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 FORM17 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
TONS PER INCH (TONS/IN)
LONGITUDINAL CENTER OF BUOYANCY (FEET)
FORWARD DRAFT MARKS (FT)
CURVE OF CENTER OF FLOTATION 20 10
Length Between Draft Marks 397' 0"
TPI KM Wo
LCB
MT1"
LCF
DRAFT FWD = 14 FT 6 IN DRAFT AFT = 16 FT 3 IN
KM = TPI = LCB = LCF =
MT1" =
22.28 FT
32.7 TONS/IN
Wo = 3850 TONS
3.5 FT AFT
778 FT-TONS/IN
24 FT AFT

74. FFG 7 10o = 15o = 20o = 30o = 40o = 45o = 50o = 55o = 60o = .55 FT
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. RIGHTING ARMS (FT) STATICAL STABILITY CURVE PLOTTING SHEET
10o = 15o = 20o = 30o = 40o = 45o = 50o = 55o = 60o =
.55 FT
.85 FT 5
1.1 FT
1.73 FT
2.35 FT 4
2.55 FT
2.6 FT
2.5 FT 3
2.3 FT X X X X X
RIGHTING ARMS (FT) 2 X X 1 X X X 10 20 30 40 50
57.3 60 70 80 90
ANGLE OF INCLINATION - DEGREES