Page 119 - Introduction to Naval Architecture

106 SEAKEEPING

two periods are equal resonance occurs and it is only the action of the
damping that prevents the amplitudes of motion becoming infinite,
The amplitudes in practice may become quite large and in that case the
master would normally change speed or course to change the period of
encounter to avoid resonance. In the general study of oscillations the
ratio of the periods of natural oscillation to that of the forcing function
is known as the tuning factor. Damping, tuning factor and magnification
are discussed in Chapter 11.
The amplitude of the pitching or heaving will also depend upon the
height of the waves. It is usual to assume that the exciting forces are
proportional to the wave height and, also, the resulting motion
amplitude. This applies whilst the motions can be approximated to by
a linear equation of motion.

Presentation of motion data
The presentation of motion data for a ship should be arranged so that
it can be applied easily to geometrically similar ships in waves of varying
amplitude. This is possible when the motions are linear, the basic
assumptions being that:
(1) Translations are proportional to the ratio of linear dimensions in
waves whose lengths vary in the same way. For geometric
similarity the speed varies so that V^/L is constant.
(2) Angular motions can be treated the same way bearing in mind
that the maximum wave slope is proportional to wave height.
(3) All motion amplitudes vary linearly with wave height.
(4) Natural periods of motion vary as the square root of the linear
dimension.

These assumptions permit the results of model experiments to be
applied to the full scale ship. In watching model experiments the
motion always seems rather 'rapid' because of the way period changes.
Thus a ^ scale model will pitch and heave in a period only a fifth of the
full scale ship. A typical presentation of heave data is as in Figure 6,3.

Figure 6.3 Response amplitude operators