Lesson1 Introduction to Stability M G B KM
Lesson-1 Introduction to Stability M G B KM B IGHT WWEEIGHT TTO N S DISPLACEMENT 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
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 G 00 DISPLACEMENT
DISPLACEMENT G B 04 DISPLACEMENT
DISPLACEMENT G B 09 DISPLACEMENT
DISPLACEMENT G B 16 DISPLACEMENT
DISPLACEMENT G B 20 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. 5 T 5 T 5 T 15 T
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 MOMENT = F x d F
VOLUME = NUMBER OF CUBIC UNITS IN AN OBJECT UNITS: CUBIC FEET CUBIC INCHES CUBIC METRES V=Lx. Bx. D V = 30 M x 20 M x 6 M V = 3600 M 3 6 M M 0 3 20 M
SPECIFIC VOLUME = VOLUME PER UNIT WEIGHT UNITS: METRE CUBIC PER TON SW = 0. 97560976 M 3/TON FW = 1. 000 M 3/TON WT = VOLUME SP. VOL WT = 3600 M 3 / 0. 97560977 M 3/T WT = 3600 M 3 X 1. 025 WT = 3698, 99 TONS T/M 3 6 M 20 M M 0 3 V = 3600 M 3
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 Metacenter Gravity Buoyancy K eel CL
STABILITY REFERENCE POINTS Mother Goose Beats CL K ids
THE CENTER OF BUOYANCY
THE CENTER OF BUOYANCY WATERLINE RESERVE BUOYANCY B B 1 B
RESERVE BUOYANCY, FREEBOARD, DRAFT AND DEPTH OF HULL WATERLINE DEPTH RESERVE BUOYANCY B FREEBOARD DRAFT
CENTER OF BUOYANCY WL BB BBB
CENTER OF BUOYANCY 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.
THE CENTER OF GRAVITY G 1 G KGo KG 1
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 1 G KGo KG 1
G 1 G KG 1 KGo
MOVEMENTS IN THE CENTER OF GRAVITY G MOVES AWAY FROM WEIGHT REMOVAL G 1 G KGo KG 1 A
G 1 KGo G G G G KG 1
MOVEMENTS IN THE CENTER OF GRAVITY G MOVES IN THE DIRECTION OF A WEIGHT SHIFT G G
G G 2
THE METACENTER
METACENTER M B THE METACENTER B 1 B 2 M 45 M M 70 B CL B 20 B 45 M 20 B 70
METACENTER BBBBBB B
METACENTER M B SHIFTS
MOVEMENTS OF 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 M 1 M 1 B 1 M M M G G G B B B
o 0 -7/10 M B CL o MOVEMENT OF THE METACENTRE
MOVEMENT OF THE METACENTRE M 20 M B CL B 20
MOVEMENT OF THE METACENTRE M 20 M 45 M B B 20 B 45 L C
MOVEMENT OF THE METACENTRE M 45 M M 70 B CL B 20 B 45 M 20 B 70
MOVEMENT OF THE METACENTRE M 45 CL M 70 B M M 90 B 20 B 45 B 90 B 70 M 20
MOVEMENTS OF 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 M M 1 B 1 G G B B WHEN B MOVES UP M MOVES DOWN.
LINEAR MEASUREMENTS IN STABILITY M GM BM G KM KG B KB CLK
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 M M G G B B K CL G Z
THE STABILITY TRIANGLE MMMM M G G B BB B K KK KK CL CC LC LCL L Z BB 1 B 1 B 1 1
Sin q = opp / hyp Where : opposite = GZ hypotenuse = GM M Sin q = GZ / GM GZ = GM x Sin q Growth of GZ a GM G Z
M G 1 G B K CL
Growth of GZ α GM M AS GM DECREASES RIGHTING ARM ALSO DECREASES G 1 G Z 1 Z
INITIAL STABILITY M G B 0 - 7° CL
OVERALL STABILITY M G B RM = GZ x Wf CL Z B 1
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
M G Z B 1 THE THREE CONDITIONS OF STABILITY POSITIVE G M B B 1 G NEUTRAL M B B 1 NEGATIVE
POSITIVE STABILITY M G B K CL
POSITIVE STABILITY M G B K CL Z B 1
NEUTRAL STABILITY G M B K CL
NEUTRAL STABILITY M B K CL G B 1
NEGATIVE STABILITY G M B K CL
NEGATIVE STABILITY G M B K CL B 1
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 ARMS (FT) RIGHTING ARM CURVE 0 10 20 30 40 50 60 70 ANGLE OF HEEL (DEGREES) WL WL W L 60° 40° 20° G Z B GZ = 1. 4 FT 80 G Z B GZ = 2. 0 FT G Z B GZ = 1 FT 90
RIGHTING ARMS (FT) ANGLE OF MAXIMUM RIGHTING ARM DANGER ANGLE 0 10 20 30 40 50 60 70 ANGLE OF HEEL (DEGREES) MAXIMUM RANGE OF STABILITY 80 WL W WL L 60° 40° 20° G Z B GZ = 1. 4 FT G Z B GZ = 2. 0 FT G Z B GZ = 1 FT 90
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 CALCULATIVELIMITINGNAVIGATIONAL MP AP 20 9 8 FP PROJ 30 9 8 7 26 5 4 30 9 8 7 20 9 8 DWL BL 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
17 16 15 14 MOMENT TO ALTER TRIM ONE INCH (FOOT-TONS) DISPLACEMENT (TONS) 800 750 13 700 650 12 600 11 550 TRANSERSE TONS METACENTER PER ABOVE BOTTOM OF KEEL INCH (FT) (TONS/IN) FORWARD DRAFT MARKS (FT) LONGITUDINAL CENTER OF BUOYANCY (FEET) 17 KM 22. 2 W o 4000 22. 3 22. 4 3500 MT 1" 22. 5 22. 6 3000 22. 7 22. 8 2550 TP I AFTER DRAFT MARKS (FT) DRAFT DIAGRAM AND FUNCTIONS OF FORM 33 32 31 30 29 28 B 5 4 3 2 1 LC 15 14 1 2 3 4 5 CURVE OF CENTER OF FLOTATION 30 20 10 F LC Length Between Draft Marks 397' 0" DRAFT FWD = 14 FT 6 IN DRAFT = 16 FT 3 IN Wo = 3850 TONS MT 1" = 778 FT-TONS/IN 16 KM = 22. 28 FT TPI = 32. 7 TONS/IN LCB = 3. 5 FT AFT LCF = 24 FT AFT 13 12 11
FFG 7 CROSS CURVES OF STABILITY CENTER OF GRAVITY ASSUMED 19. 0 FT ABOVE THE BASELINE 3. 0 RIGHTING ARMS (FT) 2. 5 50 45 2. 0 1. 5 1. 0 55 40 60 30 20 15 0. 5 3000 10 3500 4000 4500 DISPLACEMENT (TONS) 10 o =. 55 FT 15 o =. 85 FT 20 o = 1. 1 FT 30 o = 1. 73 FT 40 o = 2. 35 FT 45 o = 2. 55 FT 50 o = 2. 6 FT 55 o = 2. 5 FT 60 o = 2. 3 FT
RIGHTING ARMS (FT) 10 o =. 55 FT 15 o =. 85 FT 5 20 o = 1. 1 FT 30 o = 1. 73 FT 40 o = 2. 35 FT 45 o = 2. 55 FT 4 50 o = 2. 6 FT 55 o = 2. 5 FT 60 o = 2. 3 FT 3 STATICAL STABILITY CURVE PLOTTING SHEET X X X 2 X 1 X 0 X 10 X X 20 30 40 50 57. 3 60 70 ANGLE OF INCLINATION - DEGREES 80 90
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