A ship floats in salt water on an even keel displacing 6200 tonnes. KG 5.5m, KM 6.3m, and there is 500 tonnes of cargo yet to load. Space is available in No. 1 ‘tween deck (KG 7.6m, centre of gravity 40m forward of the centre of flotation) and in No. 4 lower hold (KG 5.5m, cen tre of gravity 30m aft of the centre of flotation). Find how much cargo to load in each space to complete loading trimmed 0.6m by the stern, and find also the final GM. MCT 1cm 200 tonnes m.

A ship floats in salt water on an even keel displacing 6200 tonnes. KG 5.5m, KM 6.3m, and there is 500 tonnes of cargo yet to load. Space is available in No. 1 ‘tween deck (KG 7.6m, centre of gravity 40m forward of the centre of flotation) and in No. 4 lower hold (KG 5.5m, cen tre of gravity 30m aft of the centre of flotation). Find how much cargo to load in each space to complete loading trimmed 0.6m by the stern, and find also the final GM. MCT 1cm 200 tonnes m.

 

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 16.9

 

Solution:

Let,

Cargo to load in No-1 = w ton

Cargo to load in No-4 = 500-w ton

weight	Distance from CF	Moment
W	-40 (F)	-40w
500-w	+30 (A)	15000-30w
∑ = 500

 

Change in trim = 15000-70w/200

=> +60 = 15000-70w/200

=> 12000 = 15000 – 70w

=> w = 42.9 ton

 Cargo to load in No-1 = 42.9 ton

Cargo to load in No-4 = 500 – 42.9 = 457.1 ton

 

GM calculation:

w	KG	moment
6200	5.5	34100
42.9	7.6	326.04
457.1	5.5	2514.05
∑ = 6700		∑ = 36940.09

 

New KG = 36940.09/6700 = 5.513 m

GM = KM – KG = 6.3 – 5.513 = 0.79 m