Page 161 - statbility for masters and mates

Trim 149
e Fig. 15.11
The moment to change trim by the head The moment to change trim by the stern.
Let the centre of ¯otation be `x' metres aft of amidships. Taking moments,
then,
100 24 x 30 30 x 60 15 x 2400 100x 900 30x 900 60x
190x 600
x 3:16m
Ans. Centre of flotation is 3.16 metres aft of amidships.
Note. In this type of question it is usual to assume that the centre of ¯otation is aft of amidships, but this may not be the case. Had it been assumed that the centre of ¯otation was aft of amidships when in actual fact it was forward, then the answer obtained would have been minus.
Remember. Levers, moments and trim by the stern all have a ve sign. Levers, moments and trim by the head all have a ve sign.
Loading a weight to keep the after draft constant
When a ship is being loaded it is usually the aim of those in charge of the operation to complete loading with the ship trimmed by the stern. Should the ship's draft on sailing be restricted by the depth of water over a dock- sill or by the depth of water in a channel, then the ship will be loaded in such a manner as to produce this draft aft and be trimmed by the stern.
Assume now that a ship loaded in this way is ready to sail. It is then found that the ship has to load an extra weight. The weight must be loaded in such a position that the draft aft is not increased and also that the maximum trim is maintained.
lf the weight is loaded at the centre of ¯otation, the ship's drafts will increase uniformly and the draft aft will increase by a number of centimetres equal to w/TPC. The draft aft must now be decreased by this amount.
Now let the weight be shifted through a distance of `d' metres forward. The ship will change trim by the head, causing a reduction in the draft aft by a number of centimetres equal to l/L Change of trim.
Therefore, if the same draft is to be maintained aft, the above two quantities must be equal. i.e.