Page 117 - statbility for masters and mates

Calculating KB, BM, and metacentric diagrams 105
For a rectangular water-plane area the second moment about the centre line is found by the formula:
I LB3 12
where L the length of the water-plane, and B = the breadth of the water- plane, (the derivation of this formula is shown in Chapter 29).
Thus, for a vessel having a rectangular water-plane area:
BM LB3 12V
For a box-shaped vessel:
BM V1
LB3 12V
L B3 12 L B draft
; BM B2 12d
where B the beam of the vessel, and d any draft of the vessel. B is a constant, d is a variable.
For a triangular-shaped prism: BM VI
LB3 12V
L B3
12 12 L B draft
; BM B2 6d
where B is the breadth at the waterline and d is the corresponding draft. B and d are variables.
Example 1
A box-shaped vessel is 24m 5m 5m and ¯oats on an even keel at 2m draft. KG 1.5 m. Calculate the initial metacentric height.