Study On The Mathematical Model Of Anchor Dropping By Its Weight

On account of its simple operation,high maneuvering characteristics and capacity of anti-wave/wind anchoring is an inescapable operation in shipping business.But safety problems are showed up during anchor dropping,some vessels have lost its anchor chain or damaged its anchor due to the unduly dropping speed.The accidents of losing anchor and chain,damaging to submarine pipelines in seabed by drooping anchor are close related to anchor dropping speeds.On account of this,it is necessary to research the speed of anchor during the dropping process.The differential equation of anchor movement and the boundary and initial conditions are set forth based on the force analysis of anchor and chain in order to know the variation and the maximum value of falling speeds.In order to get the force in the equation the gravity of anchor and chain,water-entry impact force on anchor,water resistance and additional resistance of anchor and chain,friction between chain and hawse pipe,inertial resistance and axial friction of anchor chain sprocket and chain cable fairlead,and The brake force of windlass have been analyzed.The anchoring process is divided into four parts,before anchor crown entry water,anchor striking waters,after striking waters and before chain into water,and after chain into water.The formulas of the forces in each part are given.The motion mathematic model of dropping anchor is established by substituting the formulas into the differential equation.The development of anchor dropping speed and accelerated speed is preliminary predicted by simulating calculation of three different weight anchors.Further research shows that the inertial resistance of chain grub wheel,water impact force and the additional inertial resistance of anchor and chain only impose on the history of anchor speeds,but have nothing to do with the maximum value of ones.The maximum dropping speed is primarily affected by the weights of anchor and chains,the resistances of those in water,friction between chain and hawse pipe and axial friction of anchor chain sprocket and chain cable fairlead.The establishment of the model lays the foundation for the next research on the anchor drop test and the buried depth of submarine pipeline.