Page 121 - Introduction to Naval Architecture

108 SEAKEEPING

Measured at a fixed point the wave period is T w = A/T^. If the ship is
travelling at V s at a to the direction of wave advance, in a time T E the
ship will have travelled T EV S cos a in the wave direction and the waves
will have travelled T^V^. If T E is the period of encounter the difference
in the distances must be one wave length 1, and:

If the ship travels in the same direction as the waves the period of
encounter is greater than the wave period. If it is running into the
waves the period of encounter is less.

ENERGY SPECTRA

Modification of wave energy spectrum
From the expression for T E it follows that:

If the abscissae of the 'absolute' wave spectra are multiplied by [1 -~
(a)V s/g)cos a] the abscissae of what can be called an encounter
spectrum are found. Ignoring any influence of the ship's presence on
the waves, the area under the spectrum must remain the same, that

So the ordinates of the spectrum must be multiplied by [1 - (2toV s/
1
g)cos a]' . In the case of a ship moving direcdy into the waves, that is a
- 180°, the multiplying factors become:

Obtaining motion energy spectra
The energy spectrum for any given motion can be obtained by
multiplying the ordinate of the wave encounter spectrum by the square