A ship is 150m long, displacement 12000 tonnes, and is floating at drafts of 7m F and 8m A. The ship is to enter port from an anchorage with a maximum draft of 7.6m. Find the minimum amount of cargo to discharge from a hold whose centre of gravity is 50m aft of the centre of flotation (which is amidships), TPC 15 tonnes and MCT 1cm 300 tonnes m.

 A ship is 150m long, displacement 12000 tonnes, and is floating at drafts of 7m F and 8m A. The ship is to enter port from an anchorage with a maximum draft of 7.6m. Find the minimum amount of cargo to discharge from a hold whose centre of gravity is 50m aft of the centre of flotation (which is amidships), TPC 15 tonnes and MCT 1cm 300 tonnes m.

and MCT 1cm 300 tonnes m.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 16.6

 

Solution:

Let w tons of cargo need to be discharged.

Bodily rise = w/TPC = w/15 cm

New draft AFT = 8 m – w/15 cm

Required draft = 7.6 m

 

Draft change in AFT = 8 – w/0.15 – 7.6

                                  = 0.4 – w/0.15

 

Change in trim = w*d/MCTC

                         = 50w/300

                         = w/6

 

x/t = l/L

=> x/(w/6) = ½

=> x = w/12 cm

=> x = w/0.12 m

 

Now,

0.4 – w/0.15 = w/0.12

=> w = 266.67 ton