Page 74 - Introduction to Naval Architecture
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FLOTATION AND STABILITY 61
Figure 4.24
immersed wedges which must be compensated for by a bodily rise or
sinkage. In the case illustrated the ship rises. Using subscripts e and i
for the emerged and immersed wedges respectively, the geometry of
Figure 4.24 gives:
For very small angles GZ still equates to GMq), so the slope of the GZ
curve at the origin equals the metacentric height. That is GM = dGZ/
d<p at (f = 0. It is useful in drawing a GZ curve to erect an ordinate
at (f) = I rad, equal to the metacentric height, and joining the top of
this ordinate to the origin to give the slope of the GZ curve at the
origin.
The wall-sided formula, derived earlier, can be regarded as a special
case of Atwood's formula. For the wall-sided ship:
If the ship has a positive GM it will be in equilibrium when GZ is zero,
that is:
