01 Overview of Ship Stability

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2009 Fall, Ship Stability

SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.krSeoulNationalUniv.

NavalArchitecture&O

ceanEngine

ering



Ship Stability

2009 Fall

Prof. Kyu-Yeul Lee

Department of Naval Architecture and Ocean Engineering,Seoul National University

Reference

Kyu-Yeul Lee,, Seoul National University, 2003.9


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- Contents -Part.1-I Fundamentals of Ship Stability

Ch.1 Overview of Ship Stability

Ch.2 Physics for Ship Stability

Ch.3 Hydrostatic Pressure, Force and Moment on a Floating BodyCh.4 Concept of Righting MomentCh.5 Hydrostatic Values

Part.1-II Righting MomentCh.6 Transverse Righting Moment

Ch.7 Longitudinal Righting MomentCh.8 Heeling Moment caused by Fluid in Tanks

Part.1-III Stability CriteriaCh.9 Intact StabilityCh.10 Damage Stability

Part.1-IV Pressure Integration Technique

Ch.11 Calculation of Static Equilibrium PositionCh.12 Governing Equation of Force and Moment with Immersion, Heel and TrimCh.13 Partial Derivatives of Force and Moments with Immersion, Heel and Trim

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NavalArchitecture&O

ceanEngine

ering



- Ship Stability -

Part.1-I Fundamentals of Ship Stability

2009 Fall

Prof. Kyu-Yeul Lee

Department of Naval Architecture and Ocean Engineering,

Seoul National University


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NavalArchitecture&O

ceanEngine

ering



- Ship Stability -

Ch.1 Overview of Ship Stability

2009 Fall

Prof. Kyu-Yeul Lee

Department of Naval Architecture and Ocean Engineering,

Seoul National University


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Change of Position of Ship 1. Immersion

Change of Position of Ship 1. Immersion

Immersion due to external force

d

G

B0

y

z

CL

Base

Line

G y

z

CL

Base

Line

- Overview of Ship Stability

G : Center of gravity

B : Center of buoyancy

F: Force

d: Immersion

y

z x

o

F

F

O

O x

B1

x

F

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G

CL

y

z

Change of Position of Ship 2. Heel

Heel due to external moment

B1

Change of Position of Ship 2. Heel

z

CL

Base

Line

yG

B0


B0



F: Force

: Heel Angle

y

z x

O Ox x

F

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Change of Position of Ship 3. Trim

Trim due to external moment

Change of Position of Ship 3. Trim

x

z

Base

Line

G

B0 B1

G

B0

x


yz

xo



F: Force

: Trim Angle

y

z x

o

O y O y

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Introduction to Ship Stability: Transverse Righting Moment of Ship (1)

Righting Moment : Moment to

return the ship to the upright floating

position (Moment of statical stability)

O'x'y'z': Body fixed frame

Oxyz : Waterplane fixed frame

B0

K

G

O,O'

CL

y

z

Base

Line

FG

z

y

e y

z( )+

j

k

FB

B1


x,x'

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Introduction to Ship Stability: Transverse Righting Moment of Ship (2)

Z

K

z

y

z M

restoring

e

G

FG

BB1

N

FB

1By

Gy

O'x'y'z': Body fixed frame

Oxyz : Waterplane fixed frame

BGZ F= i Transverse Righting moment

1( )restoring G B By y F = + i

Righting arm

Righting Arm (GZ)

1G BGZ y y= +

From direct calculation

We should knowyG, yB1 in waterplane fixed frame

From geometrical figure withassumption that Mdoes not changewithin small angle of heel (about 10)

sinGZ GM =

GM is related to below equation bygeometrical figure

GM KB BM KG= + - Overview of Ship Stability

y

z( )+

j

k

O,O'

x,x'

Righting Moment : Moment to

return the ship to the upright floating

position (Moment of statical stability)

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Introduction to Ship Stability: Stability Criteria IMO Regulations for Intact Stability

100 30 4020 50 60 70 80

Angle of heel

()

Righting Arm

(GZ(m))

A B

(a) Area A 0.055 m-rad

Area A : Heel Angle from 0~ 30

Area B : Heel Angle from 30~ min(40,f )

f : An angle of heel at whichopenings in the hull

m : Angle of maximum righting arm

(c) Area B 0.030 m-rad

(d) GZ 0.20 m at an angle of heel equal to or greater than 30

(b) Area A + B 0.09 m-rad

(e) GZmax should occur at an angle of heel equal to or greater than 25.

(f) The initial metacentric height GMo should not be less than 0.15 m.

(IMO Res.A-749(18) chapt.3.1)

m

After receiving approval of

calculation of IMO regulation from

Owner and Classification Society,

ship construction can proceed.- Overview of Ship Stability

= const

IMO Regulations for Intact Stability

( :displacement)

f

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Righting Moment

Overview of Ship Stability

Force & Moment on a Floating BodyNewtons 2nd LawEuler Equation

Stability Criteria

Damage Stability- MARPOL regulation

Pressure Integration Technique

Calculation Method to find GZwith respect to IMO regulation

sinGZ GM = ,GM KB BM KG= +

sinL LGZ GM = , L LGM KB BM KG= +


BF GZ

Transverse RightingMoment :

B LF GZ

Longitudinal RightingMoment :

GZ Calculation

( )G BGZ y y= +

( )L G B

GZ x x= +

Z

K

z

O

CL

y

z M

restoring

e

G

FG

BB1

N

FB

1By

Gy

FB: Buoyancy force

: Angle of Heel, : Angle of Trim

(xG,yG,zG) : Center of gravity in waterplane fixed frame(xB,yB,zB) : Center of buoyancy in waterplane fixed frame

y'G, y'B in body fixed frame

Rotational Transformation!

yG, yB in waterplane fixed frame

Fundamental of Ship Stability

Properties which is related to hullform of the ship

Hydrostatic Values

Intact Stability- IMO Requirement (GZ)- Grain Stability- Floodable Length

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P d F i Fl id P i l

Assumption

di l t f ti l ith t t ti


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SDAL@Advanced Ship Design Automation Lab.SeoulNational2009 F ll Shi S bili

-Pressure and Force acting on Fluid Particle-6 D.O.F Equations of Ship Motions: Relations among Undergraduate Lectures

12/15112/131

6 D.O.F equations of motions

Shear force(S.F.) &

bending moment(B.M.)

Shear force(S.F.)

Integral

Bending moment(B.M.)

Coordinate system(Waterplane Fixed & Body-fixed frame)

Newtons 2nd Law

( ) ( , , )gravity Fluid = +F r F r r r

)()( ForceSurfaceForceBody +=

Calculation of

Fluid Force

Equations of motions

of Fluid Particles

Cauchy

equation

Navier-Stokes

equation

MEuler

equation

Bernoulli

equation

02

1 2=+++

zgP

t

Mass

Conservation

Law02 =

Laplace

Equation

LinearizationR

D

I

+

+

= (Incident wave potential)

(Diffraction potential)

(Radiation potential)

Shear stress Curl & Rotation

Lagrangian &

Eulerian Description

Enigneering Math.(2nd-year undergraduate)

( )=V

Velocity potential

1) RTT : Reynold Transport Theorem

2) SWBM : Still Water Bending Moment

3) VWBM : Vertical Wave Bendidng Moment

Assumption

FF.K: Froude- krylov force

FD: Diffraction force

FR: Radiation force

Gravityz faxm ,)(

BS dSPnt

gzP

=

( , , )Fluid =F r r r .( ) ( ) ( ) ( , , )Buoyancy F K D R= + + +F r F r F r F r r r

Microscopic/

Macroscopic Derivation(RTT1))

= 0

2

1 2

(az : Acceleration of

z directionby heave& pitch motion)

Newtons 2nd Law(Body force

Surface force)

m = =

+

r Fm

Staticz

zDKF

fvb

aaff

,

,,,

33

33..

Ship Hydrodynamics, Dynamics(2nd-year undergraduate)

.

, ,

( ) ( ) ( )

( , ) ( , )

gravity Buoyancy F K D

R Damping R Mass

= + + +

+ +

F F r F r F r

F r r F r r

Non-linear terms Non-linear equation

Difficulty of getting analytic solution

Numerical Method Computer aided ship design(3rd-year undergraduate)

Newtonian fluid*

invicid fluid

Stokes Assumption**

Irrotational flow

Incompressible flow

[ ]1 2 3 4 5 6, , , , , T

=r

1

2

3

:

:

:

surge

sway

heave

4

5

6

, :

, :

, :

roll

pitch

yaw

y

z

( : wetted surface)BS

1x ..FS..MB

x

z

= Mr F

Ship Structural Design system(3rd -year undergraduate)

Fundamental of maritimeStructural statics(2nd -year undergraduate)

Behavior of ship and its control(3rd -year undergraduate)

Dynamics (2nd -year undergraduate)

Planning procedure ofnaval architecture and

ocean engineering(2nd-year undergraduate)

Ocean environment

Information system(3rd -year undergraduate)

2

2

: displacement of particle with respect to time

,d d

dt dt = =

r

r rV a

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Documents

01 Overview of Ship Stability