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Q2. The 'wall sided formula' gives an expression for righting lever (GZ) as follows:

GZ = sinq (GM + ½ BM tan2q)

(a) Derive an expression for the 'angle of loll’ of a ship which is initially unstable in still water, using the wall sided formula.

(b) A box shaped vessel is 80 m long, 12 m wide and floats at a draught of 5 m in sea water of density 1025 kg/m3 with a KG of 4.815 m.

A beam wind acts on the exposed area of the vessel causing it to heel to an angle of 15°.

The heeling moment caused by the wind is given

Heeling moment= 0.85 Ab v² cos² 8 Nm

where: A = exposed area = 627 m²

b = lever = 6.5 m

v = wind speed in m/s

e = angle of heel in degrees.

Calculate the wind speed using the wall sided formula for GZ.