Page 100 - Introduction to Naval Architecture

THE ENVIRONMENT H7

only a compound of a number of regular systems, individually of
comparatively small amplitude, and covering a range of periods.
Further he stated that the effect of such a compound wave system on a
ship would be 'more or less the compound of the effects proper to the
Individual units composing it'. This is the basis for all modern studies
of waves and ship motion. Unfortunately the mathematics were not
available in 1905 for Froude to apply his theory. That had to wait until
the early 1950s.
Since the individual wave components are regular it is necessary to
study the properties of regular waves.

Regular waves
A uni-directional regular wave would appear constant in shape with
time and resemble a sheet of corrugated iron of infinite width. As it
passes a fixed point a height recorder would record a variation with
time that would be repeated over and over again. Two wave shapes are
of particular significance to the naval architect, the trochoidal wave and
the sinusoidal wave.

The trochoidal wave
By observation the crests of ocean waves are sharper than the troughs.
This is a characteristic of trochoidal waves and they were taken as an
approximation to ocean waves by early naval architects in calculating
longitudinal strength. The section of the wave is generated by a fixed
point within a circle when that circle rolls along and under a straight
line, Figure 5.1.

Figure 5.1 Trochoidal wave

The crest of the wave occurs when the point is closest to the straight
line. The wavelength, A, is equal to the distance the centre of the circle
moves in making one complete rotation, that is A = 2 nR. The
waveheight is 2r = h w. Consider the *-axis as horizontal and passing
though the centre of the circle, and the z-axis as downwards with origin
at the initial position of the centre of the circle. If the circle now rolls