Solution Naval Numerical 13

Numerical 13: A ship of 8000 tonne displacement floats upright in seawater. KG = 7.6m and GM = 0.5m. A tank, KG is 0.6m above the keel and 3.5m from the centreline, contains 100 tonne of water ballast. Neglecting the free surface effect, calculate the angle which the ship will heel, when the ballast water is pumped out.

Solution: as the 100t  mass is removed from the ship in the form of ballast water, the total displacement is reduced and KG has become high.

Angle of list can be fine by using

---(i)

heeling moment =mxd =100 x3.5 =350 t-m

final displacement(△f) =8000-100=7900 t

  =KM - =KG+GM -

=(8000x7.6 -100x0.6)/7900 = 7.698m

thus,   = 7.6+0.5 - 7.698=0.411m

 thus, from (i)

Tanθ=350/7900x0.411

θ =6.152 degrees.