right of resonance. Thus, even without the precise value for the damp- 
ing coefficient, it is possible to estimate with confidence the heave 
response for this particular platform to incident waves with periods 
up to, say, 15 seconds. 
Figures 3.11 through 3.12 depict the heave response for the same 
platform for three assumed irregular sea states using the Neumann 
windwave spectrum. Each of these plots shows the heave response of 
the subject platform in both a "light" and a "heavy" load condition for 
a single assumed Neumann wind velocity (30 and 40 knots). Even at 
the highese sea state investigated, the platform exhibits a small motion 
relative to the height of the incident sea. 
One is cautioned about extending this approach to higher sea states 
for at least two reasons: 
1. The equations of motion have been linearlized and, thus, 
should not be applied too far beyond the domain of ''small amplitude" 
waves. 
2. The platform heave response curve, i. e., the platform 
response to regular waves, is at present, imprecisely known around 
resonance. This fact begins to have importance at higher sea states 
since the energy contained in the wave spectrum tends to shift towards 
lower frequencies and to concide with the heave response curve at 
resonance. Since the heave spectrum is obtained by forming the product 
of the square of the heave response curve and the ordinate of the wave 
amplitude spectrum at the same frequency, the uncertain value of the 
platform heave response near and at resonance tends to create uncertainty 
as well as in the heave spectrum. 
The total vertical movement at any point on the platform is a 
superposition of the pure heave response and the vertical movement due 
to pitch and roll. The investigation into the effects of the latter are 
not complete and therefore are not included in this report. 
An elevated platform having constant diameter cylindrical legs for 
buoyant support is perhaps the easiest configuration for analysis. 
Other platform types, e. g., elevated platforms with bulbous legs, semi- 
submersibles and barges, are also amenable to analysis. The principal 
difficulty lies in determining the damping and added-mass coefficients 
by analysis or experiment. 
3-28 
