Page 119 - statbility for masters and mates

Example 3
Ans. GM 1:58 m
Calculating KB, BM, and metacentric diagrams 107
The second moment of a ship's water-plane area about the centre line is 20 000 m4 units. The displacement is 7000 tonnes whilst ¯oating in dock water of density 1008 kg per cu. m. KB 1.9 m, and KG 3.2 m. Calculate the initial metacentric height.
Volume of water displaced 7000 1000 cu. m 6944 cu. m 1008
BM VI
; BM 20 000
6944 BM 2:88m
KB 1:90 m KM 4:78m KG 3:20m
Metacentric diagrams
It has been mentioned in Chapter 6 that the of®cer responsible for loading a ship should aim to complete the loading with a GM which is neither too large nor too small. See table of typical GM values on p. 49 for merchant ships when fully loaded. A metacentric diagram is a ®gure in graph form from which the KB, BM, and thus the KM can be found for any draft by inspection. If the KG is known and the KM is found from the diagram, the difference will give the GM. Also, if a ®nal GM be decided upon, the KM can be taken from the graph and the difference will give the required ®nal KG.
The diagram is usually drawn for drafts between the light and loaded displacements, i.e. 3 m and 13 m respectively overpage.
Figure 12.5 shows a metacentric diagram drawn for a ship having the following particulars:
Draft (m)
13 12 11 10
9 8 7 6 5 4 3
KB (m)
6.65 6.13 5.62 5.11 4.60 4.10 3.59 3.08 2.57 2.06 1.55
KM (m)
11.60 11.30 11.14 11.10 11.15 11.48 11.94 12.81 14.30 16.63 20.54
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