Lesson-1
Introduction to Stability
CL
M
G
B
K
BM
KM
DISPLACEMENT
TONS
WEIGHT
TON S
WEIGHT
B
G
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
Definitions :• Stability
• Initial Stability
• Overall Stability
• Dynamic Stability
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
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.
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.
DISPLACEMENT
• THE WEIGHT OF THE VOLUME OF WATERTHAT 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
DISPLACEMENT
00
G
DISPLACEMENT
DISPLACEMENT
04
G
B
DISPLACEMENT
DISPLACEMENT
09
G
B
DISPLACEMENT
DISPLACEMENT
16
G
B
DISPLACEMENT
DISPLACEMENT
20
G
B
DISPLACEMENT
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
WEIGHT : GRAVITATIONAL FORCE. DIRECTION TOWARD CENTER OF EARTHUNITS : TONS, POUNDS, etc
MOMENT: THE TENDENCY OF A FORCE TO PRODUCE ROTATION ABOUT AN AXIS
MOMENT = F x d
ad F
VOLUME = NUMBER OF CUBIC UNITS IN AN OBJECTUNITS: CUBIC FEET CUBIC INCHES CUBIC METRESV = L x B x D
20 M30 M
6 M
V = 30 M x 20 M x 6 MV = 3600 M3
SW = 0.97560976 M3/TONFW = 1.000 M3/TON
SPECIFIC VOLUME = VOLUME PER UNIT WEIGHT
UNITS: METRE CUBIC PER TON
20 M30 M
6 MV = 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
CLASS TOPICS1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings7. Draft Diagram and Cross Curves8. Model
2. Stability Reference Points
• Metacentre• Gravity• Buoyancy• Keel
STABILITY REFERENCE POINTS
CL
M
G
B
K
etacenter
ravity
uoyancy
eel
STABILITY REFERENCE POINTS
CL
otherM
ooseG
eatsB
idsK
THE CENTER OF BUOYANCY
B
WATERLINERESERVE BUOYANCY
B
THE CENTER OF BUOYANCY
B1
WATERLINE
B
RESERVE BUOYANCY
RESERVE BUOYANCY, FREEBOARD, DRAFTAND DEPTH OF HULL
DRAFT
FREEBOARD
DEPTH
CENTER OF BUOYANCY
B
WLWL
B
WL
B
WL
B
WL
B
CENTER OF BUOYANCY
BBBBBBBB
B
THE CENTER OF GRAVITY
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.
GG1
KGo
KG1
THE CENTER OF GRAVITY
G
G1
KGo
KG1
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
MOVEMENTS IN THE CENTER OF GRAVITY
• G MOVES TOWARDS A WEIGHT ADDITION
G
G1
KGo
KG1
G
KGo
G1
KG1
MOVEMENTS IN THE CENTER OF GRAVITY
G MOVES AWAY FROM A WEIGHT REMOVAL
GG1
KGo
KG1
GGGGGGG1
KG1
KGo
G
MOVEMENTS IN THE CENTER OF GRAVITY
G MOVES IN THE DIRECTION OF A WEIGHT SHIFT
G G
G2
G
THE METACENTER
THEMETACENTER
CL
B
B20B45
M
M20
M45
M70
B70
METACENTER
M
BB1 B2
METACENTER
BBBBBBBBB
METACENTER
B SHIFTS
M
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.
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
CL
B
M
0o-7/10o MOVEMENT OF THE METACENTRE
CL
B B20
M
M20
MOVEMENT OF THE METACENTRE
CL
M
M20
M45
B
B20 B45
MOVEMENT OF THE METACENTRE
CL
B
B20
B45
M
M20
M45
M70
B70
MOVEMENT OF THE METACENTRE
CL
M20M45
M70
M90
B
B20
B45B70
B90
M
MOVEMENT OF THE METACENTRE
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.
G
B
G
M
B
M1
B1
MOVEMENT OF THE METACENTRE
G
WHEN B MOVES UP M MOVES DOWN.
GM
KG
CLK
M
G
B
BM
KM
LINEAR MEASUREMENTS IN STABILITY
KB
CLASS TOPICS1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings7. Draft Diagram and Cross Curves8. Model
3. Stability Triangle
M
G Z
M
G ZCL
K
B
G
M
THE STABILITY TRIANGLE
CL
K
B
G
M
CL
K
B
G
MM
CL
G
B
K
B1
CL
M
G
B
K
B1
CL
M
G
B
K
B1
CL
K
B
G
M
B1
Z
THE STABILITY TRIANGLE
M
G Z
Where :opposite = GZ
hypotenuse = GM
Sin = GZ / GM
GZ = GM x Sin
Growth of GZ GM
Sin = opp / hyp
CL
K
B
G
M
G1
G
M
Z
G1 Z1
AS GM DECREASES RIGHTING ARM ALSO DECREASES
Growth of GZ α GM
INITIALSTABILITY
G
B
M
0 - 7°CL
M
ZG
B B1
CL
OVERALLSTABILITY
RM = GZ x Wf
CLASS TOPICS1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings7. Draft Diagram and Cross Curves8. Model
G
B1
M
Z
G
B1
M
B
G
B1
M
B
THE THREE CONDITIONS OF STABILITY
POSITIVE
NEUTRAL
NEGATIVE
CL
K
B
G
M
POSITIVE STABILITY
CL
K
B
G
M
B1
Z
POSITIVE STABILITY
CL
K
B
GM
NEUTRAL STABILITY
CL
K
BB1
NEUTRAL STABILITY
GM
CL
K
B
G
M
NEGATIVE STABILITY
CL
K
B
GM
B1
NEGATIVE STABILITY
CLASS TOPICS1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings7. Draft Diagram and Cross Curves8. Model
RIG
HT
ING
AR
MS
(F
T)
ANGLE OF HEEL (DEGREES)9060300 10 20 40 50 70 80
WL20°
G
B
Z
WL
40°
G
B
Z
WL
60°
G
B
Z
GZ = 1.4 FT GZ = 2.0 FT GZ = 1 FT
RIGHTING ARM CURVE
RIG
HT
ING
AR
MS
(F
T)
ANGLE OF HEEL (DEGREES)9060300 10 20 40 50 70 80
WL
WL
20°
G
B
Z
WL
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
DANGERANGLE
MAXIMUM RANGE OF STABILITY
CLASS TOPICS1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings7. Draft Diagram and Cross Curves8. Model
DWL
BL
LONGITUDINAL CROSS SECTION
FPAP MP
LBP
20 9 8
30 9 8 7
20 9 8
30 9 8 7
26 5 4
PROJ
CALCULATIVE NAVIGATIONALLIMITING
CLASS TOPICS1. Definitions
2. Stability Reference Points
3. Stability Triangle
4. Conditions of Stability
5. Stability Curve
6. Ship’s Hull Markings7. Draft Diagram and Cross Curves8. Model
DRAFT DIAGRAM AND FUNCTIONS OF FORM
17
16
15
14
13
12
11
8004000
3500
3000
2550
750
700
650
600
550
AFTERDRAFTMARKS
(FT)
MOMENT TOALTER TRIM
ONE INCH(FOOT-TONS) DISPLACEMENT
(TONS)
22.2
22.322.422.5
22.622.722.8
TRANSERSE METACENTERABOVE BOTTOM OF KEEL (FT)
2829
30
31
32
3354321
12345
11
12
13
14
15
16
17
TONSPERINCH
(TONS/IN)
LONGITUDINALCENTER OFBUOYANCY
(FEET)
FORWARDDRAFTMARKS
(FT)
CURVE OF CENTER OF FLOTATION
30 20 10
Length Between Draft Marks 397' 0"
DRAFT FWD = 14 FT 6 INDRAFT AFT = 16 FT 3 IN
W o
Wo = 3850 TONS
KM =TPI =LCB =LCF =MT1" =
MT1"
778 FT-TONS/IN
KM
22.28 FTTP
I32.7 TONS/IN
LCB
3.5 FT AFT
LCF
24 FT AFT
FFG 7CROSS CURVES OF STABILITY
CENTER OF GRAVITY ASSUMED19.0 FT ABOVE THE BASELINE
DISPLACEMENT (TONS)
RIG
HT
ING
AR
MS
(F
T)
3000 3500 4000 4500
40
30
20
15
10
60
5545
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 FT1.1 FT1.73 FT2.35 FT2.55 FT2.6 FT2.5 FT2.3 FT
0
1
2
3
4
5STATICAL STABILITY CURVE PLOTTING SHEETR
IGH
TIN
G A
RM
S (
FT
)10o =15o =20o =30o =40o =45o =50o =55o =60o =
.55 FT
.85 FT1.1 FT1.73 FT2.35 FT2.55 FT2.6 FT2.5 FT2.3 FT
X
XX
X
X
XX X X
X
10 20 30 40 50 57.3 60 70 80 90
ANGLE OF INCLINATION - DEGREES
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