Page 115 - Introduction to Naval Architecture
P. 115
102 SEAKEEPING
Figure 6.1 Rolling
By Newton's laws, this moment will impart an angular acceleration,
such that:
This is the standard differential equation denoting simple harmonic
motion with a period T v, defined by:
where ^ is the radius of gyration about a fore and aft axis.
This period is independent of (p and such rolling is said to be
isochronous. The relationship holds for most ships up to angles of about
10° from the vertical. It will be noted that the greater GM T the shorter
the period. A ship with a short period of roll is said to be stiff and one
with a long period of roll is termed tender. Most people find a slower
motion, that is a tender ship, less unpleasant.
Pitching
This is controlled by a similar equation to that for roll. In this case:
