A STUDY ON SHIP MOTIONSBYM VIVEK REDDY, 10NA30014

UNDER GUIDANCE OF PROF. VISHWANATH NAGARAJAN

OVERVIEWIntroductionModellingHeave-pitch couplingStrip TheoryResultsBeam Rolling ResultsConclusion Future work

INTRODUCTION

Of the six motions of the ship, the roll oscillation is the most critical motion that can lead to the ship capsizing.

For a head sea condition, the roll response becomes important as the water plane area changes drastically as the wave passes which influences the roll restoring coefficient

As the heave motions and pitch motions also contribute to the changes in the water plane area, roll motion is to be simulated along with its coupling with heave and pitch motions

OBJECTIVETo calculate the Roll-Heave-Pitch coupled response of the vessel for a head sea conditionTo establish Heave, Pitch and Roll RAOs of the vessel and to compare them with the RAOs obtained from SEAKEEPER module of MaxsurfAnalyse the regions of roll instability

DOLNETER-4

MeasurementValueLength Overall18.52 mBreadth5.64 mDraft2 mCb0.533

MODELLING

LINES PLAN OF DOLNETER-4

HYDROSTATIC CALCULATIONS

MeasurementValueDisplacement98.564 tonnesVolume96.16 m3LCB0.74 m aft of MSLCF1.323 m aft of MSWSA115.31 m2KG2.2 m (from empirical estimation1)GMt0.469 mGML12.869 m

HEAVE PITCH COUPLING EQUATIONS

STRIP THEORYStrip theory considers a ship to be made up of a finite number of transverse two dimensional slices, which are rigidly connected to each other.Each slice is treated hydrodynamically as if it is a segment of an infinitely long floating cylinder.

STRIP THEORY CONTD.Radiation Forces data is available for 2-D ship like sections

3 basic 2-D methods are :Ursell s analytical solution of the potential theory for a circular cross section.Conformal mapping of a ship - like cross section to the unit circle and Tasai s extension of Ursells theory to con formal mapped cross sections.Frank s pulsating source theory , directly applied to a ship-like cross section

CHARTS FOR OBTAINING 2D POTENTIAL COEFFICIENTS

ESTIMATING ADDED MASS AND DAMPING COEFFICIENTS

ESTIMATING ADDED MASS AND DAMPING COEFFICIENTS

ESTIMATED VALUES OF COEFFICIENTS AT V=0

QuantityValuesA3384.6 tA44237.71 t-m^2A551599 t-m^2B33161.5 t/sB44278.21 t-m^2/sB553811.3 t-m^2/sA35=A53183 t-mB35=B53420.4 t-m/sC33735.7 t/s^2C44543.2 tm^2/s^2C5513588 tm^2/s^2C35=C53394 t-m/s^2

TIME PERIODSNatural Time Periods (dry)Theave = 2.31 secTpitch =2.34 secTroll =6.37 sec

Wet Time periods (wet for =1.879 rad/sec)Theave = 3.1426 secTpitch =3.1845 secTroll =7.61 sec

HEAVE RESPONSE, V=0

PITCH RESPONSE, V=0

HEAVE RESPONSE, V=8 KNOTS

PITCH RESPONSE , V=8 KNOTS

ROLL EQUATION

BEAM ROLL RESPONSE, V=0

PRESENT CONCLUSIONNatural Time Periods for heave, pitch , roll are establishedHeave and pitch response for an incident wave is calculated Beam roll response for a given wave is calculated

FUTURE WORKCalculation of non linear Froude Krilov and Diffraction exciting forces and MomentsSimulate Coupled Heave-Pitch-Roll motions in Head sea conditionComparison of manually calculated RAOs with the RAOs obtained from SEAKEEPER module of MaxsurfAnalyse the regions of roll instability

REFERENCES[1]Fishing Vessels by Jacob PinksterDynamics of Marine Vehicles by Rameshwar BhattacharyaDynamics of Marine Craft by Edward M lewandowskiPractical Ship Hydrodynamics by Volker Bertram

APPENDIX