Naval Architecture & Ocean Engineering

2009 Fall, Ship Stability

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

Seoul NationalUniv.

Nav

al A

rchi

tect

ure

& O

cean

Eng

inee

ring


Seoul NationalUniv.


Ship Stability

2009 Fall

Prof. Kyu-Yeul Lee

Department of Naval Architecture and Ocean Engineering,Seoul National University

Reference Kyu-Yeul Lee, 선박안정론, Seoul National University, 2003.9



Seoul NationalUniv.

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

Ch.1 Overview of Ship StabilityCh.2 Physics for Ship StabilityCh.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 MomentCh.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 TechniqueCh.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

2/12



Seoul NationalUniv.

Nav

al A

rchi

tect

ure

& O

cean

Eng

inee

ring


Seoul NationalUniv.


- Ship Stability -

Part.1-I Fundamentals of Ship Stability

2009 Fall

Prof. Kyu-Yeul Lee




Seoul NationalUniv.

Nav

al A

rchi

tect

ure

& O

cean

Eng

inee

ring


Seoul NationalUniv.


- Ship Stability -

Ch.1 Overview of Ship Stability

2009 Fall

Prof. Kyu-Yeul Lee




Seoul NationalUniv.

Change of Position of Ship – 1. Immersion

Change of Position of Ship – 1. Immersion

Immersion due to external force

d

G

B0

y

z

CLBaseLine

G y

z

CL

BaseLine

- Overview of Ship Stability

G : Center of gravityB : Center of buoyancyF : Forced : Immersion

yz x

o

F

F

OO 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

CLBaseLine

yG

B0


B0

G : Center of gravityB : Center of buoyancyF : Forceφ : Heel Angle

φ

yz 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

BaseLine

G

B0 B1

G

B0

x


yzxo

θ

G : Center of gravityB : Center of buoyancyF : Forceθ : Trim Angle

y

z xo

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 frameOxyz : Waterplane fixed frame

B0

K

G

O,O'

CL

y

z

BaseLine

FG

z′

y′

eτ τy

z( )+j

k

FB

B1


x,x'

8/12



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

Z≡

K

z′

y

z M

φ

restoringτ

eτ

G

FG

B B1

≡ NFB

≡

1By

Gy

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

BGZ F= ⋅ i• Transverse Righting moment

1( )restoring G B By y Fτ = − + ⋅ i

Righting arm

φ

φ

• Righting Arm (GZ)

1G BGZ y y= − +① From direct calculation

We should know yG, yB1 in waterplane fixed frame② From geometrical figure with

assumption that M does not change within small angle of heel (about 10°)

sinGZ GM φ= ⋅

GM is related to below equation by geometrical figure

GM KB BM KG= + −- Overview of Ship Stability

τy

z( )+j

k

O,O'x,x'

• Righting Moment : Moment to return the ship to the upright floating position (Moment of statical stability)

9/12



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

100 30 4020 50 60 70 80Angle of heel

(φ)

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°, φ f )※ φf : An angle of heel at which

openings in the hull

φm : 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)

φm

※ 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)

φf

10/12



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Righting Moment

Overview of “Ship Stability”

Force & Moment on a Floating BodyNewton’s 2nd Law Euler Equation

Stability Criteria

Damage Stability- MARPOL regulation

Pressure Integration Technique

Calculation Method to find GZ with respect to IMO regulation

sinGZ GM φ= ,GM KB BM KG= + −

sinL LGZ GM θ= , L LGM KB BM KG= + −


BF GZ×Transverse Righting Moment :

B LF GZ×Longitudinal Righting Moment :

<Method ②>

GZ Calculation

( )G BGZ y y= − +

( )L G BGZ x x= − +

<Method ①>

Z≡

K

z′

O

CL

y

z M

φ

restoringτ

eτ

G

FG

B B1

≡ NFB

≡

1By

Gy

φ

φ

FB: Buoyancy forceφ : Angle of Heel, θ : 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 hull form of the ship

Hydrostatic Values

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

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Seoul NationalUniv.2009 Fall, Ship Stability

-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.)

① Coordinate system(Waterplane Fixed & Body-fixed frame)

② Newton’s 2nd Law

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

)()( ForceSurfaceForceBody +=

Calculation of Fluid Force

Equations of motionsof Fluid Particles

Cauchyequation

Navier-Stokesequation

MEuler

equationBernoulliequation

021 2 =+Φ∇++

∂Φ∂ zgPt

ρρρMass

ConservationLaw

02 =Φ∇LaplaceEquation

LinearizationR

D

I

Φ+Φ+Φ=Φ (Incident wave potential)

(Diffraction potential)

(Radiation potential)

③

④⑤

④⑤①②

Shear stress Curl & Rotation

Lagrangian & Eulerian Description

Enigneering Math.(2nd-year undergraduate)

( )Φ∇=V

Velocity potential Φ

1) RTT : Reynold Transport Theorem2) SWBM : Still Water Bending Moment3) VWBM : Vertical Wave Bendidng Moment

Assumption

FF.K: Froude- krylov forceFD: Diffraction forceFR: Radiation force

Gravityz faxm ,)(−

∫∫BS

dSPnt

ρgzP∂Φ∂

−−= ρ

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

Microscopic/Macroscopic Derivation(RTT1))

=Φ∇ 0

21 2ρ

(az : Acceleration of z direction

by heave& pitch motion)

Newton’s 2nd Law(Body force

Surface force)m = =

+∑r Fm

Staticz

zDKF

fvbaaff

,,,,

33

33..

−−

Ship Hydrodynamics, Dynamics(2nd-year undergraduate)

.

, ,

( ) ( ) ( )

( , ) ( , )gravity Buoyancy F K D

R Damping R Mass

= + + +

+ +

F F r F r F rF 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)

① Newtonian fluid*

③ invicid fluid② Stokes Assumption**

④ Irrotational flow⑤ Incompressible flow

[ ]1 2 3 4 5 6, , , , , Tξ ξ ξ ξ ξ ξ=r1

2

3

:::

surgeswayheave

ξξξ

4

5

6

, :, :, :

rollpitchyaw

ξξξ

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 andocean engineering(2nd-year undergraduate)

Ocean environment Information system(3rd -year undergraduate)

2

2

: displacement of particle with respect to time

,d ddt dt

= =

rr rV a

12/12

Naval Architecture & Ocean Engineering

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