A ship of 8000 tones displacement takes the ground on a sand bank on a filing tide at an even keel draft of 5.2 meters. KG 4.0 meters. The predicted depth of water over the sand bank at the low water is 3.2 meters. Calculate the GH at this time assuming that the KM will then be 5.0 meters and that the mean TPC is 15 tone.

P = TPC x fall in water level (cm)

= 15 x (520 – 320)

= 3000 tonnes.

Method (a)

Virtual loss GM (MM1) = P x KM / W

= 3000 x 5 / 8000 = 1.88m

Actual KM = 5.00 m

Virtual KM = 3.12 m

KG = 4.00 m

Answer New GM = - 0.88 m

Method (b)

Virtual loss GM (GG1) = P x KG / W – P

= 3000 X 4 / 5000

= 2.40 M

KG = 4.00 m

Virtual KG = 6.40 m

KM = 5.00 m

Answer New GM = - 1.40 m

Note that in example, this vessel has developed a negative GM. Consequently she is unstable. She would capsize if transverse external forces such as wind or waves were to remove her from zero angle of heel. Suggest a change of loading to reduce KG and make GM a positive value greater than DfT minimum of 0.15m.