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How does the direction of approaching velocities of ships affect berthing?

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One of the major effects of angle of approaching velocities of ships is its influence of the energy to be absorbed by the fender system. Consider several ships berth on the same pier at the same speed but with different angle of approach, though their kinetic energies are the same, the amount of energy absorbed by fender differs. The amount of energy absorbed by fender is :

approaching velocities of ships

where W= energy absorbed by the fender
m= mass of the ship
v=velocity of the ship
k= radius of gyration of the ship
r= distance of centre of gravity of the ship to the point of contact of the fender

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Hence, when the direction of approaching velocity of a ship is normal to the fender system (i.e. phi=90 ), the amount of energy absorbed is smaller when compared with that of a ship whose velocity is tangential to the shoreline.

This question is taken from book named – A Self Learning Manual – Mastering Different Fields of Civil Engineering Works (VC-Q-A-Method) by Vincent T. H. CHU.

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