Page 106 - Introduction to Naval Architecture

THE ENVIRONMENT 93

where:

p(h) = the height of curve, the frequency of occurrence
h = wave height
h = mean wave height from record
£i = standard deviation
Where data are from a record of say 30 minutes duration, during
which time conditions remain reasonably steady, a Rayleigh distribution is
found to be a better fit. The equation for this type of distribution is:

where:

In these expressions p(h) is a probability density, the area under the
curve being unity because it is certain that the variable will take some
value of h. The area under the curve between two values of h represents
the probability that the waveheight will have a value within that range.
Integrating the curve leads to a cumulative probability distribution. The
ordinate at some value h on this curve represents the probability that
the waveheight will have a value less than or equal to h.
For more information on these and other probability distributions
the reader should refer to a textbook on statistics,

Energy spectra
One of the most powerful means of representing an irregular sea and,
incidentally, a ship's responses as will be discussed in Chapter 6, is the
concept of an energy spectrum. The components of the sea can be
found by Fourier analysis and the elevation of the sea surface at any
point and time can be represented by:

h = S&n cos (a) n + e n )

where hn, a) n and e n are the height, circular frequency and arbitrary
phase angle of the nth wave component.
The energy per unit area of surface of a regular wave system is
proportional to half the square of the wave height. The energy