lesson-1 introduction to stability cl m g b k bm km displacement t o n s w e i g h t t o n s w e i g...

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




5. Stability Curve

6. Ship’s Hull Markings7. Draft Diagram and Cross Curves8. Model


• 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


• G MOVES TOWARDS A WEIGHT ADDITION

G

G1

KGo

KG1

G

KGo

G1

KG1


G MOVES AWAY FROM A WEIGHT REMOVAL

GG1

KGo

KG1

GGGGGGG1

KG1

KGo

G


G MOVES IN THE DIRECTION OF A WEIGHT SHIFT

G 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


CL

M

M20

M45

B

B20 B45


CL

B

B20

B45

M

M20

M45

M70

B70


CL

M20M45

M70

M90

B

B20

B45B70

B90

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.

G

B

G

M

B

M1

B1


G

WHEN B MOVES UP M MOVES DOWN.

GM

KG

CLK

M

G

B

BM

KM

LINEAR MEASUREMENTS IN STABILITY

KB





5. Stability Curve



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





5. Stability Curve


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





5. Stability Curve


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





5. Stability Curve


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





5. Stability Curve


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

lesson-1 introduction to stability cl m g b k bm km displacement t o n s w e i g h t t o n s w e i g...

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