Roll Motion of Ships - 160.75.46.2160.75.46.2/staff/taylan/ms/6_Roll Motion.pdfRoll Motion of Ships...

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Roll Motion of ShipsRoll Motion of Ships

ShipShip MotionsMotions

OscillatoryOscillatory shipship motionmotion ::

3 3 translatorytranslatory ((surgesurge, , swaysway andand heaveheave))3 3 rotationalrotational ((rollroll, , pitchpitch andand yawyaw))

© Metin Taylan, 2010© Metin Taylan, 2010

6 6 DoFDoF ShipShip MotionsMotions


Ship MotionsShip Motions


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Ship MotionsShip Motions


Equation of MotionEquation of Motion•• Equilibrium of all forces acting on the rigid Equilibrium of all forces acting on the rigid

ship in the 3 translatory directions, xship in the 3 translatory directions, x11, x, x22and xand xand xand x33

•• Equilibrium of all moments acting on the Equilibrium of all moments acting on the rigid ship in the 3 rotational directions, xrigid ship in the 3 rotational directions, x44, , xx55 and xand x66

321i0F


3,2,1i0Fi

i

6,5,4i0Mi

i

Equation of MotionEquation of Motionship reaction = external excitationship reaction = external excitation

61idxcxbxa 6,...,1idxcxbxa ijijjijjij

t/ffdi tiimotionyoscillatorofonacceleratix

motionyoscillatorofvelocityxmotionshipyoscillatorx


tscoefficiencouplingthegiveijjidirectionmotionj

moment/forceofdirectioni

Equation of MotionEquation of Motion

inertiainertia forceforce/moment/moment dependingdepending on on thetheoscillatoryoscillatory motionmotion accelerationacceleration ofof thethe shipshipxa oscillatoryoscillatory motionmotion accelerationacceleration of of thethe shipshipbodybody

damping damping forceforce/moment/moment dependingdepending on on thethe motionmotion velocityvelocity

restoringrestoring forceforce/moment/moment dependingdepending on on thth ti lti l ill till t titi

xb

cx


thethe particularparticular oscillatoryoscillatory motionmotion xxdd externalexternal excitationexcitation forceforce/moment/moment duedue totothethe seawayseaway

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Equation of MotionEquation of MotionCoupled roll with heave and pitch :Coupled roll with heave and pitch :

xcxbxa4jiRollxcxbxa3jHeave 343343343

i=4i=4 moment equation for rollmoment equation for rolljj direction (mode) of motiondirection (mode) of motion In order solve the above coupled equationIn order solve the above coupled equation

dxcxbxa5jPitchxcxbxa4jiRoll

545545545

344444444


In order solve the above coupled equation In order solve the above coupled equation (= to estimate roll angle x), we must (= to estimate roll angle x), we must additionally solve the equation for heave additionally solve the equation for heave (i=3) and for pitch (i=5)(i=3) and for pitch (i=5)

Equation of MotionEquation of MotionIf we rewrite the above equation; If we rewrite the above equation;

dMxcxbxa c4344444444

MM4c4c :sum of all coupling moments for i=4 from :sum of all coupling moments for i=4 from the motion directions j other than 4. the motion directions j other than 4. Disregarding coupling Disregarding coupling MM4c4c=0 =0 (uncoupled roll (uncoupled roll motion):motion):

dcba


dcba

inertia termdamping term

restoring termexciting term

Equation of MotionEquation of MotionCoefficients of the equation :Coefficients of the equation :

aa inertia coefficientinertia coefficientbb damping coefficientdamping coefficientcc restoring coefficientrestoring coefficientdd external roll excitation (wind, waves etc.)external roll excitation (wind, waves etc.)


Mass moment of inertiaMass moment of inertiaInertia coefficient Inertia coefficient aa is defined as :is defined as :

T2

T 'i'Ia TTT ''II'I

I’I’TT Total mass moment of inertia of the rolling ship Total mass moment of inertia of the rolling ship IITT mass moment of inertia of the shipmass moment of inertia of the shipI’’I’’TT added mass moment of inertiaadded mass moment of inertiaΔΔ displacement massdisplacement mass

TT iIa


ppρρ water densitywater densityi’i’TT roll radius of gyrationroll radius of gyration

4

Radius of GyrationRadius of Gyration•• i’i’TT is the radius of a solid ring, which replaces is the radius of a solid ring, which replaces

the total mass of the ship as shown in the the total mass of the ship as shown in the figurefigurefigure. figure.

•• This radius is enlarged by the inertia effect of This radius is enlarged by the inertia effect of the surrounding water with respect to roll the surrounding water with respect to roll acceleration, the soacceleration, the so--called hydrodynamic mass called hydrodynamic mass moment or added mass moment moment or added mass moment I’’I’’TT


RadiusRadius of of GyrationGyration


Linear Restoring MomentLinear Restoring MomentFor large heel, the static restoring moment is:For large heel, the static restoring moment is:

GZgMst


Linear Restoring MomentLinear Restoring MomentFor most ships at small heel up to about 5 For most ships at small heel up to about 5 degrees the gradient degrees the gradient GMGMΦΦ is constantis constant

dGZ

The parameter The parameter cc in the roll equation, is the in the roll equation, is the ““spring constantspring constant” (” (restoring coefficientrestoring coefficient) :) :

)0(d

dGZGM0

.deg5forGMGZ 0 00 GMsinGMGZ


spring constantspring constant ( (restoring coefficientrestoring coefficient) :) :

0B00st GMFGMg

GMgMc

5

StiffStiff ShipShip vs. Tender vs. Tender shipship

•• When the initial stability is large (When the initial stability is large (GMGM00 is is large) the ship is called “large) the ship is called “stiffstiff” i e she is not” i e she is notlarge) the ship is called large) the ship is called stiffstiff” i.e she is not ” i.e she is not sensitive to small heeling moments.sensitive to small heeling moments.

•• For small initial metacentric height, the For small initial metacentric height, the ship is “ship is “tendertender” i e the ship is sensitive to” i e the ship is sensitive to


ship is ship is tendertender i.e. the ship is sensitive to i.e. the ship is sensitive to small heeling momentssmall heeling moments

StiffStiff ShipShip vs. Tender vs. Tender shipship


RollRoll MotionMotion


SpringSpring--MassMass Damper Damper SystemSystem andand RollRoll


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Natural Roll PeriodNatural Roll PeriodCircular roll frequency :Circular roll frequency :

20

GMgGMgc

It is practical to refer to the natural roll period :It is practical to refer to the natural roll period :

2T

2T

0 'i'ia

T1fandf2

000

2f1T


•• The natural roll period, The natural roll period, TT0 0 can be estimated with the can be estimated with the ship at free roll in still water condition using a stopwatchship at free roll in still water condition using a stopwatch

•• IMO requires the average of about 5 cycles be takenIMO requires the average of about 5 cycles be taken

T 00

Roll DampingRoll DampingThe oscillating free rolling motion eventually dies The oscillating free rolling motion eventually dies

out. Free roll transfers the roll energy to the out. Free roll transfers the roll energy to the surrounding water by potential and frictionsurrounding water by potential and frictionsurrounding water by potential and friction surrounding water by potential and friction forces. The decay of the roll is due to dampingforces. The decay of the roll is due to damping


Roll DampingRoll Damping0cba

With the initial condition (at t=0) With the initial condition (at t=0) ΦΦ = = ΦΦ0 0 and and ddΦΦ/dt =0, the differential equation becomes :/dt =0, the differential equation becomes :

WhWh

0ac

ab


Where;Where;

acand

ab2 2

0

Roll DampingRoll Damping

The solution of free rolling motion :The solution of free rolling motion :

02 20

For small damping, the frequency For small damping, the frequency ωωΦΦ of of the free roll can be approximated by the the free roll can be approximated by the

tcostexp 00


natural frequency natural frequency ωω0 0 from;from;

1Das)D1( 20

220

2

7

Roll DampingRoll DampingFrom the solution;From the solution;

texp

The ratio of 2 successive roll amplitudes The ratio of 2 successive roll amplitudes ΦΦn n and and ΦΦn+1n+1 at a distance of the natural period Tat a distance of the natural period T0 0 is : is :

p0

nn0n TexpTt


1n1n01n TexpTt

)Texp()TT(exp

TexpTexp

0n1nn0

1n0

n

1n

Roll DampingRoll Damping

)Texp( 01n

n

The dimension of The dimension of δδ is sis s--11. In order to define . In order to define a dimensionless damping parameter;a dimensionless damping parameter;

1n

n

0

lnT1


1ssD 1

1

0

Roll DampingRoll DampingThe dimensionless damping,The dimensionless damping,

ca2/bD

•• To estimate the damping paramater D, To estimate the damping paramater D,

1n

n0

0

ln21

2T

D


successive roll amplitudes at one side are successive roll amplitudes at one side are to be measured and put into the equation.to be measured and put into the equation.

•• For most ship For most ship D D ≤ 0.10≤ 0.10

Rolling Period TestRolling Period TestRolling coefficient :Rolling coefficient :

B50'iC T

r

After necessary manipulations;After necessary manipulations;B5.0r

GMBC

GMgB5.0C2

GMg'i22T rrT

00


gg0

GMBCT r

0

8

Rolling Period TestRolling Period TestThe practical importance of the above The practical importance of the above relationship lies in estimating the relationship lies in estimating the matacentric height GM by conducting thematacentric height GM by conducting thematacentric height GM by conducting the matacentric height GM by conducting the rolling period test. rolling period test.

2

0

r

TBCGM


Weiss formula, 1953Weiss formula, 1953

0

Rolling Period TestRolling Period Test


Rolling Period TestRolling Period Test•• The rolling period test should be The rolling period test should be

conducted with the ship in harbour in conducted with the ship in harbour in smooth water with the minimumsmooth water with the minimumsmooth water with the minimum smooth water with the minimum interference from the wind and tide. interference from the wind and tide.

•• The ship can be made to roll by rhytmically The ship can be made to roll by rhytmically lifting up and putting down a weight or lifting up and putting down a weight or people running athwartships (people running athwartships (sallying sallying experimentexperiment))


experimentexperiment))•• The initial roll amplitude for the measured The initial roll amplitude for the measured

roll decay should not exceed 5roll decay should not exceed 500

Rolling Period TestRolling Period Test•• IMO allows estimating the stability by IMO allows estimating the stability by

means of rolling period tests for small means of rolling period tests for small ships of up to 70 m in lengthships of up to 70 m in lengthships of up to 70 m. in lengthships of up to 70 m. in length

•• IMO Resolution A.749(18) was adopted on IMO Resolution A.749(18) was adopted on 4 November 1993.4 November 1993.

•• However, the rolling period test must be However, the rolling period test must be seen as a very simplified method when noseen as a very simplified method when no


seen as a very simplified method, when no seen as a very simplified method, when no other stability information is available.other stability information is available.

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Rolling Period TestRolling Period TestThe Weiss formula gives GM as a function of;The Weiss formula gives GM as a function of;

•• Natural roll period, TNatural roll period, T00

•• Beam of the vessel, BBeam of the vessel, B•• Rolling coefficient, CRolling coefficient, Crr


Rolling Period TestRolling Period TestFor Coasters of normal size, the observed CFor Coasters of normal size, the observed Crrvalues are;values are;

•• Empty ship or carrying ballastEmpty ship or carrying ballast 0.880.88•• Ship fully loaded with liquids in tanksShip fully loaded with liquids in tanks 0.880.88•• Comprising 20% of total loadComprising 20% of total load 0.780.78•• Comprising of 5% of total loadComprising of 5% of total load 0 730 73


•• Comprising of 5% of total loadComprising of 5% of total load 0.730.73

Rolling Period TestRolling Period TestIMO Resolution A.749(18) (1993) and IMO IMO Resolution A.749(18) (1993) and IMO Circular 707 (1995) present an approximate Circular 707 (1995) present an approximate formula from statistics:formula from statistics:formula from statistics:formula from statistics:

100L043.0

TB023.0373.0C5.0 2


BGMT

C 0r

Different Modes of Roll ExcitationDifferent Modes of Roll ExcitationRoll excitation for a for a ship in a seaway:Roll excitation for a for a ship in a seaway:

1.1. Time varying Time varying external excitationexternal excitation in the rightin the right--hand side of the equationhand side of the equation

2.2. Time varying Time varying parametric excitationparametric excitation in the in the leftleft--hand side of the equationhand side of the equation


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Different Modes of Roll ExcitationDifferent Modes of Roll Excitation•• A ship in beam seas can experience large roll A ship in beam seas can experience large roll

with large inertia forces acting on the cargo.with large inertia forces acting on the cargo.•• Following and stern quartering seas at the same Following and stern quartering seas at the same

bili b d i hbili b d i hstability can be more dangerous with respect to stability can be more dangerous with respect to capsizing and loss of the ship.capsizing and loss of the ship.

•• An excitation due to time variation of ship An excitation due to time variation of ship reaction is called parametric. At parametric reaction is called parametric. At parametric resonance, the ship is in danger of capsizing.resonance, the ship is in danger of capsizing.

•• This is mostly seen in certain condition in This is mostly seen in certain condition in longit dinal and stern q artering seaslongit dinal and stern q artering seas


longitudinal and stern quartering seas.longitudinal and stern quartering seas.•• Both external and parametric excitations exist Both external and parametric excitations exist

simultaneously in quartering seas.simultaneously in quartering seas.

Ship Rolling in Beam SeasShip Rolling in Beam SeasThere are only external excitation in beam seas There are only external excitation in beam seas written on the rigthwritten on the rigth--hand side of the equation.hand side of the equation.

dynamic reaction + static reaction = external excitationdynamic reaction + static reaction = external excitation

For small amplitudes,For small amplitudes,Roll motion equation is a linear second order Roll motion equation is a linear second order


differential equation. differential equation.

Ship Rolling in Beam SeasShip Rolling in Beam Seas

FB : bouyancy force

The amplitude of beam sea excitation;


AABAA GMgGMFcd

)tsin(dd A

)tsin(GMgd A

At the wave trough :

Wave Slope vs. Distance from CrestWave Slope vs. Distance from Crest

The wave slope is the first derivative of the wave ordinate with respect to the distance x from the wave crest in the travelling


respect to the distance x from the wave crest in the travelling direction of the wave.

)cos(5.0)( kxHx w

kxsinkH5.0x

)x( w

Wave ordinate :

Wave slope :

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Wave SlopeWave SlopeWave slope amplitude :Wave slope amplitude :

)(25.0

5.0 radLH

LH

kH wwwA

The exciting moment in beam seas:The exciting moment in beam seas:

I hi i h ll i iI hi i h ll i i

LL ww

)tsin(LH

GMgdw

w


Insert this into the roll motion equation:Insert this into the roll motion equation:

A

A3V

Transfer function Amplitude of roll

Amplitude of wave slope

Solution of the EquationSolution of the EquationThe solution is the equation is given by the The solution is the equation is given by the transfer function Vtransfer function V33 which is the dynamic which is the dynamic amplification factor;amplification factor;amplification factor;amplification factor;

The dimensionless wave frequency with The dimensionless wave frequency with respect to the natural roll frequency is therespect to the natural roll frequency is the

222234)1(

1)(

D

V


respect to the natural roll frequency is the respect to the natural roll frequency is the tuning factor tuning factor ηη ;;

0w

0

TT

Solution of the EquationSolution of the EquationThe The dimensionless damping Ddimensionless damping D ::

nln21

ac2bD

Rewite transfer function;Rewite transfer function;

Th l i ll i i bTh l i ll i i b

1n0 2ac2

22220

20

34)(

)(

V


The resulting roll motion in beam seas:The resulting roll motion in beam seas:

)tsin(V 33A

Solution of the EquationSolution of the Equation

The The phase angle phase angle γγ33 between the exciting moment d between the exciting moment d and the roll:and the roll:and the roll:and the roll:

1

D2arctan 23


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ResonanceResonance

Less sensitive to wave excitation


Very sensitive to wave excitation

Transfer Function of Roll in Beam SeasTransfer Function of Roll in Beam Seas


Important Results from the SolutionImportant Results from the Solution1.1. The static heel The static heel ωω = 0 results from = 0 results from

constant excitation independent of time:constant excitation independent of time:At t3 1)0(V

2.2. With the exciting wave frequency, With the exciting wave frequency, ωω, , increasing there is a steady increase of increasing there is a steady increase of the roll response:the roll response:

Astat3 1)0(V

TT1


The dynamic response is always greater The dynamic response is always greater than the static heel than the static heel VV33 > 1> 1

0w0 TT1

Important Results from the SolutionImportant Results from the Solution

3.3. There is dominant amplification in the There is dominant amplification in the region around region around ηη=1 (resonance).=1 (resonance).Th f f th k iTh f f th k iThe frequency of the peak response is :The frequency of the peak response is :

The resonant roll amplitude at the peak is: The resonant roll amplitude at the peak is:

022

0r 2


AA0

r D21

2

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Important Results from the SolutionImportant Results from the Solution4.4. In the frequency range above resonance, we observe In the frequency range above resonance, we observe

a rapid decrease of the roll responsea rapid decrease of the roll response

TT1

The larger natural period TThe larger natural period T00 of the ship corresponds to of the ship corresponds to a small GM, and we have a tender ship.a small GM, and we have a tender ship.

5.5. At very large wave frequency At very large wave frequency ωω, the dynamic roll , the dynamic roll response is less than the static heel angle, it response is less than the static heel angle, it

0w0 TT1


p g ,p g ,approaches zero approaches zero VV33 00. Therefore, at little or very . Therefore, at little or very small GM, when small GM, when TT00 >> T>> Tww, the ship experiences little of , the ship experiences little of almost no roll amplification in purely beam seasalmost no roll amplification in purely beam seas

Roll in Beam Seas at Large AmplitudesRoll in Beam Seas at Large AmplitudesWe subdivide the roll amplitudes into regions:We subdivide the roll amplitudes into regions:

Small rollSmall roll ΦΦAA ≤ 5≤ 500 GMGMΦΦ = GM = const= GM = constSmall roll, Small roll, ΦΦAA ≤ 5≤ 5 GMGMΦΦ = GM = const.= GM = const.Large roll, Large roll, ΦΦAA > 5> 500 GMGMΦΦ increasing fromincreasing from

GMGM00 to GMto GMmaxmaxLarge rollLarge roll GMGMΦΦ decreasing fromdecreasing from

GMGMmaxmax to GMto GMΦΦ =0=0


maxmax ΦΦExtreme rollExtreme roll GMGMΦΦ <0, <0,

i.e. above GZi.e. above GZmaxmax

Roll in Beam Seas at Large AmplitudesRoll in Beam Seas at Large Amplitudes

•• For larger roll amplitudes, more For larger roll amplitudes, more mathematical effort is needed in order to mathematical effort is needed in order to solve the equation of roll motionsolve the equation of roll motionsolve the equation of roll motion. solve the equation of roll motion.

•• For extreme roll including capsize, For extreme roll including capsize, numerical time domain simulations with numerical time domain simulations with step by step integration of the roll motion step by step integration of the roll motion equation have been developed with good equation have been developed with good


results.results.•• At large roll in beam seas:At large roll in beam seas:

)cos( tdcba

Roll in Beam Seas at Large AmplitudesRoll in Beam Seas at Large Amplitudes•• The restoring term is approximated by a The restoring term is approximated by a

cubic function :cubic function :3

31 ccc

•• This solution gives the calculated This solution gives the calculated nonlinear transfer function for 2 different nonlinear transfer function for 2 different GZ curves.GZ curves.

•• The nonlinear solution shows also a The nonlinear solution shows also a resonance peak as in the linear case butresonance peak as in the linear case but


resonance peak as in the linear case, but resonance peak as in the linear case, but now it is bent to one side (now it is bent to one side (jump jump phenomenonphenomenon).).

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Roll in Beam Seas at Large AmplitudesRoll in Beam Seas at Large Amplitudesa.a. CC22 > 0 GZ over> 0 GZ over--linearlinear : curve bends to : curve bends to

larger larger ωω (right)(right)

b.b. CC22 < 0 GZ under< 0 GZ under--linearlinear : curve bends to : curve bends to smaller smaller ωω (left)(left)


Roll in Beam Seas at Large AmplitudesRoll in Beam Seas at Large AmplitudesOver-linear roll response Under-linear roll response


GZ Variations in Longitudinal WavesGZ Variations in Longitudinal Waves

•• A ship in longitudinal waves experiences a A ship in longitudinal waves experiences a completely different shape of the completely different shape of the underwater volume as compared with theunderwater volume as compared with theunderwater volume as compared with the underwater volume as compared with the ship in still water and in beam seas. ship in still water and in beam seas.

•• The righting moment of the vessel varies The righting moment of the vessel varies in time with the passing wave.in time with the passing wave.

•• This results in a dynamic excitation of rollThis results in a dynamic excitation of roll


This results in a dynamic excitation of roll This results in a dynamic excitation of roll motionmotion

GZ Variations in Longitudinal WavesGZ Variations in Longitudinal Waves

After-body midship Fore-body


Ship in longitudinal wave at different positions relative to the crest

Wave length = LWL

Draft : full load draft

Heel angle = 300

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Comparison of GZ CurvesComparison of GZ Curves


Comparison of GZ CurvesComparison of GZ Curves•• The change of GZ results from the change The change of GZ results from the change

in the location of the center of bouyancy B in the location of the center of bouyancy B of the heeled ship hull in the longitudinalof the heeled ship hull in the longitudinalof the heeled ship hull in the longitudinal of the heeled ship hull in the longitudinal wave.wave.

•• Weight force, W and the center of gravity, Weight force, W and the center of gravity, G remain constantG remain constant


GZ Changes in Longitudinal WaveGZ Changes in Longitudinal Wave


Wave Crest SituationWave Crest Situation•• The freeboard amidships reduces considerably.The freeboard amidships reduces considerably.•• It may even become negative.It may even become negative.

D t l k f b b th d k id tD t l k f b b th d k id t•• Due to lack of buoyancy above the deck side at Due to lack of buoyancy above the deck side at large heel, the center of buoyancy in heeled large heel, the center of buoyancy in heeled condition Bcondition BΦΦ shifts towards the center of gravity shifts towards the center of gravity G.G.

•• This shift of B reduces GZThis shift of B reduces GZ


•• Freeboards at sections 1 and 3 increase but Freeboards at sections 1 and 3 increase but cannot counteract the GZ reduction amidshipscannot counteract the GZ reduction amidships

•• Thus overall reduction in GZ resultsThus overall reduction in GZ results

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Wave Trough SituationWave Trough Situation

•• The wave trough amidships results an The wave trough amidships results an i f th i hti l GZi f th i hti l GZincrease of the righting lever GZ.increase of the righting lever GZ.

•• The effective freeboard of the midship The effective freeboard of the midship section 2 is considerably increasedsection 2 is considerably increased

•• The overall GZ reduction in the crest is The overall GZ reduction in the crest is larger than the gain in the troughlarger than the gain in the trough


larger than the gain in the trough.larger than the gain in the trough.

Influence of Wave Length on GZ in a Wave CrestInfluence of Wave Length on GZ in a Wave Crest


GZ reduction between still water and wave crest

Wave HeightWave HeightFormula derived from wave statistics in the North Formula derived from wave statistics in the North Atlantic:Atlantic:

1H)meterinL(

L05.0101

LH

www

w


Effect of Speed on GZ CurvesEffect of Speed on GZ Curves•• Blume and Hattendorf (1982) compared the Blume and Hattendorf (1982) compared the

hydrostatic results with measurements on hydrostatic results with measurements on models of container ships in following seas.models of container ships in following seas.

•• For Froude Numbers between 0 For Froude Numbers between 0 –– 0.28 there 0.28 there was almost no difference in GZ.was almost no difference in GZ.

•• At FAt Fnn = 0.36 the reduction in the wave crest = 0.36 the reduction in the wave crest was about half the value of the hydrostatic was about half the value of the hydrostatic calculationcalculation


•• At FAt Fnn = 0.36 the increase in the wave trough = 0.36 the increase in the wave trough was about 10% less than the hydrostatic was about 10% less than the hydrostatic result.result.

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Effect of Speed on GZ CurvesEffect of Speed on GZ Curves


C Factor C Factor •• Blume and Hattendorff (1982, 1984) developed Blume and Hattendorff (1982, 1984) developed

a soa so--called Ccalled C--Factor for usual merchant hull Factor for usual merchant hull forms which allows including the GZ reductionforms which allows including the GZ reductionforms, which allows including the GZ reduction forms, which allows including the GZ reduction in waves by a formula based on capsizing in waves by a formula based on capsizing model experiments.model experiments.

•• IMO implemented the CIMO implemented the C--factor for container factor for container ships and fast ships with a small Cships and fast ships with a small CBB (0.554(0.554--


p pp p B B ((0.675) into IMO stability criteria (IMO, 1993)0.675) into IMO stability criteria (IMO, 1993)

C FactorC Factor

BP

2

w

B2 L

100cc

KGT

B'DTC

TT mean draft (m)mean draft (m)BB moulded breadth of the ship (m)moulded breadth of the ship (m)KGKG height of the center of gravity (m)height of the center of gravity (m)

not to be taken less than Tnot to be taken less than T


not to be taken less than Tnot to be taken less than TCCBB block coefficientblock coefficientCCww waterplane coefficientwaterplane coefficient

C FactorC Factor

•• D’D’ effective freeboard accounts for the effective freeboard accounts for the volume of the hatches above deck amidships volume of the hatches above deck amidships (from plus and minus L/4 of the main section). (from plus and minus L/4 of the main section).

•• Ship length is to be Ship length is to be ≥ 100 m.≥ 100 m.•• KG is to be larger than draft T.KG is to be larger than draft T.•• The smaller the CThe smaller the C--factor , the larger are the factor , the larger are the

th GZ l i dth GZ l i d


the GZ values required.the GZ values required.•• IMO asks for hydrostatic values in the form of IMO asks for hydrostatic values in the form of

a required constant divided by Ca required constant divided by C

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Intact stability Criteria Based on Intact stability Criteria Based on C FactorC Factor


GZ Curve Required by IMO Based GZ Curve Required by IMO Based on C Factoron C Factor


EncounterEncounter PeriodPeriod of of ShipShip andandWavesWaves

The The encounter period, Tencounter period, TEE is the time elapsed is the time elapsed from wave crest to the next wave crest passingfrom wave crest to the next wave crest passingfrom wave crest to the next wave crest passing from wave crest to the next wave crest passing the shipthe ship


EncounterEncounter PeriodPeriod of of ShipShip andand WavesWaves


19

Encounter Period of Ship and Encounter Period of Ship and WavesWaves

cosVcVrel

cosVcL

VL

T w

rel

wE

www

w fLTL

c


w

wT2gc

Encounter Period of Ship and Encounter Period of Ship and WavesWaves

2ww T

2gL

cosV2T

TT

2w

E

2 cosVg

Tw

2gL

c w

cosVL

2g

LT

w

wE


The encounter frequency:The encounter frequency:

)Hz(T1f

EE )s/rad(f2 EE

Encounter Frequency

Wave direction V

V

V180 0

90

45

V


gVw

we cos 2

direction wave the torelative angle heading sship'

(m/s) speed ship Vfrequency wave

frequencyencounter

w

e

Encounter FrequencyExample

ship speed = 20 knots, heading angle = 120 degreewave direction : from north to south, wave period=12 secondsEncountering frequency ?

Wave frequency : sradsTw / 52.0

1222

Encountering angle : o60120180 120°N


V=20kts60

Encountering freq. :

srad

gVw

we

/38.014.052.0 81.9

60cos)(10.29)52.0(52.0

cos

2

2

)/29.1020( smknotsV

S

20

Ship Heading Ship Heading

0 0 degreesdegrees following seasfollowing seas4545 degreesdegrees stern quartering seasstern quartering seas45 45 degreesdegrees stern quartering seasstern quartering seas90 90 degreesdegrees starboard beam seasstarboard beam seas180 180 degreesdegrees head seashead seas

© Metin Taylan, 2010© Metin Taylan, 2010 © Metin Taylan, 2010© Metin Taylan, 2010


Passive Anti-Rolling Device

RollRoll MotionMotion ReductionReduction

• Bilge KeelV i ti lli d i- Very common passive anti-rolling device

- Located at the bilge turn- Reduce roll amplitude up to 35 %.

• Tank Stabilizer (Anti-rolling Tank)- Reduce the roll motion by throttling the fluid

in the tankBilge keel


in the tank.- Relative change of G of fluid will dampen the roll.

ThrottlingU-type tube

21

Bilge Bilge KeelKeel LengthLength


Bilge Bilge KeelKeel ConstructionConstruction


For large ships

Active Anti-Rolling Device

Roll Motion ReductionRoll Motion Reduction

• Fin StabilizerStab e- Very common active anti-rolling device- Located at the bilge keel.- Controls the roll by creating lifting force .

Roll moment


Lift

Anti-roll moment

Fin Stabilizer


22

Ship Operation

Roll Motion ReductionRoll Motion Reduction

• Encountering frequencyheave

gVw

we cos 2

• Ship response can be reduced by altering the

heave

roll

pitch


• Ship response can be reduced by altering the- ship speed- heading angle or- both

Roll Motion of Ships - 160.75.46.2160.75.46.2/staff/taylan/ms/6_Roll Motion.pdfRoll Motion of Ships...

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