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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
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
Seoul NationalUniv.
2009 Fall, Ship Stability
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
2009 Fall, Ship Stability
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
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
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
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
Seoul NationalUniv.
2009 Fall, Ship Stability
- 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
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
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
Seoul NationalUniv.
2009 Fall, Ship Stability
- Ship Stability -
Ch.1 Overview of Ship Stability
2009 Fall
Prof. Kyu-Yeul Lee
Department of Naval Architecture and Ocean Engineering,Seoul National University
2009 Fall, Ship Stability
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
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
5/12
2009 Fall, Ship Stability
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
Seoul NationalUniv.
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
- Overview of Ship Stability
B0
G : Center of gravityB : Center of buoyancyF : Forceφ : Heel Angle
φ
yz x
O Ox x
F
6/12
2009 Fall, Ship Stability
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
Seoul NationalUniv.
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
- Overview of Ship Stability
yzxo
θ
G : Center of gravityB : Center of buoyancyF : Forceθ : Trim Angle
y
z xo
O y O y
7/12
2009 Fall, Ship Stability
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
Seoul NationalUniv.
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
- Overview of Ship Stability
x,x'
8/12
2009 Fall, Ship Stability
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
Seoul NationalUniv.
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
2009 Fall, Ship Stability
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
Seoul NationalUniv.
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
2009 Fall, Ship Stability
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
Seoul NationalUniv.
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= + −
- Overview of Ship Stability
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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2009 Fall, Ship Stability
SDAL@Advanced Ship Design Automation Lab.http://asdal.snu.ac.kr
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
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