Page 112 - statbility for masters and mates

100 Ship Stability for Masters and Mates
Fig. 12.1(b). Triangular-shaped vessel
Fig. 12.1(c). Ship-shaped vessel
and 0.49 draft. A closer approximation of thus depth can be obtained by using Morrish's Formula, which states:
Depth of centre of buoyancy below waterline 1 d V 32A
where
and
d Mean draft
V Volume of displacement
A Area of the water-plane
The derivation of this formula is as follows:
In Figure 12.2, let ABC be the curve of water-plane areas plotted against
drafts to the load waterline. Let DE V/A and draw EG parallel to the base cutting the diagonal FD in H.
It must ®rst be shown that area DAHC is equal to area DABC. Rectangle AH Rectangle HC
and
but
; Triangle AGH Triangle HEC
Area AHCD Area AGED Area AGED V/A A
V
Area DABC V
; Area DAHC Area DABC