Q. Direction of approaching velocities of ships during berthing?

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

W = 0.5mv²(k²+ r² cos²?) / (k²+ r²)

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

  Φ=direction of velocity

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