Page 76 - Introduction to Naval Architecture

FLOTATION AND STABILITY 63

Metacentric height in the lolled condition
Continuing with the wall-side assumption, if <pi is the angle of loll, the
value of GMfor small inclinations about the loll position, will be given
by the slope of the GZ curve at that point. Now:

Unless <pi is large, the metacentric height in the lolled position will
be effectively numerically twice that in the upright position although of
opposite sign.

Cross curves of stability
Cross curves of stability are drawn to overcome the difficulty in defining
waterlines of equal displacement at various angles of heel.

Figure 4.26

Figure 4.26 shows a ship inclined to some angle <p. Note that S is not
the same as in Figure 4.24. By calculating, for a range of waterlines, the
displacement and perpendicular distances, SZ, of the centroids of these
volumes of displacement from the line W through S, curves such as
those in Figure 4.27 can be drawn. These curves are known as cross