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Chapter 12
Calculating KB, BM,
and metacentric diagrams
THE method used to determine the ®nal position of the centre of gravity was examined in the previous chapter. To ascertain the GM for any condition of loading it is necessary also to calculate the KB and BM (i.e. KM) for any draft.
To ®nd KB
The centre of buoyancy is the centre of gravity of the underwater volume. For a box-shaped vessel on an even keel, the underwater volume is rectangular in shape and the centre of buoyancy will be at the half-length,
on the centre line, and at half the draft as shown in Figure 12.1(a). Therefore, for a box-shaped vessel on an even keel: KB 12 draft.
Fig. 12.1(a). Box-shaped vessel
For a vessel which is in the form of a triangular prism as shown in Figure 12.1(b) the underwater section will also be in the form of a triangular prism. The centroid of a triangle is at 2/3 of the median from the apex. Therefore the centre of buoyancy will be at the half-length, on the centre line, but the KB 2/3 draft.
For an ordinary ship the KB may be found fairly accurately by Simpson's Rules as explained in Chapter 10. The approximate depth of the centre of buoyancy of a ship below the waterline usually lies between 0.44 draft
