Page 123 - statbility for masters and mates

Calculating KB, BM, and metacentric diagrams 111
Therefore, the answer to part (a) of the question is: Minimum KM 4.08 m occurring at 4.08 m draft
To ®nd the BM at 3.5 m draft, measure the distance DE on the scale and it will give the BM (2.38 m).
Therefore, the answer to part (b) of the question is: BM at 3.5m draft 2:38m
To show that, for a box-shaped vessel, the minimum KM and the draft at which
p
it occurs are both given by the expression B/ 6, where B is equal to the
vessel's beam.
For a box-shaped vessel:
For minimum KM:
KM KB BM
d B2 KM 2 12d dKM 1 B2
dd 2 12d2
dKM O dd
;O 1 B2 2 12d2
B2 6d2 p
d B= 6
I
and
Substituting in equation (I) above:
minimum KM
p minimum KM B= 6
Figure 12.6(b) shows a metacentric diagram for a triangular-shaped underwater form with apex at the base. Note how the KM values have produced a straight line instead of the parabolic curve of the rectangular hull form. Note also how BM increases with every increase in draft.
2 p BB6
p
2 6 12B
6B 6B p
12 6