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

CLASS TOPICS Definitions Stability Reference Points Stability Triangle Conditions of Stability Stability Curve Ship’s Hull Markings Draft Diagram and Cross Curves 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 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

DISPLACEMENT DISPLACEMENT 00 G

DISPLACEMENT DISPLACEMENT 04 G B

DISPLACEMENT DISPLACEMENT 09 G B

DISPLACEMENT G B DISPLACEMENT 16

DISPLACEMENT G B DISPLACEMENT 20

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

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

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

SPECIFIC VOLUME = VOLUME PER UNIT WEIGHT UNITS: METRE CUBIC PER TON SW = 0.97560976 M3/TON FW = 1.000 M3/TON WT = VOLUME SP.VOL WT = 3600 M3 / 0.97560977 M3/T 20 M 30 M 6 M V = 3600 M3 WT = 3600 M3 X 1.025 T/M3 WT = 3698,99 TONS

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

2. Stability Reference Points Metacentre Gravity Buoyancy Keel

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

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

THE CENTER OF BUOYANCY

THE CENTER OF BUOYANCY B WATERLINE RESERVE BUOYANCY B B1

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

CENTER OF BUOYANCY WL B WL B WL B WL B WL B

CENTER OF BUOYANCY B B B B 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.

G G1 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 G G1 KGo KG1

G1 KG1 KGo G G G G G G G

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

G G2

THE METACENTER

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

METACENTER B B B B B B B B B

METACENTER M B SHIFTS

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 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

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

MOVEMENT OF THE METACENTRE M20 M B B20 CL

MOVEMENT OF THE METACENTRE M20 M45 M B B20 B45 CL

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

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

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.

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

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

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. Stability Triangle M G Z

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

THE STABILITY TRIANGLE CL 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

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

G1 M G B K CL

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

INITIAL STABILITY G B M 0 - 7° CL

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

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

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

POSITIVE STABILITY M G B K CL

POSITIVE STABILITY M Z G B B1 K CL

NEUTRAL STABILITY G M B K CL

NEUTRAL STABILITY G M B B1 K CL

NEGATIVE STABILITY G M B K CL

NEGATIVE STABILITY G M B B1 K CL

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

RIGHTING ARM CURVE RIGHTING ARMS (FT) 10 20 30 40 50 60 70 80 90 10 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

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

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

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

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

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 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

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

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