Analyses of Multiple-Float-Supported Platforms in Waves 



The corresponding frequencies f (cycles per second), for full 

 scale and model, are also related by Froude's law 



f„ = xf (46) 



f.s. f—r- m 



Results 



Vertical wave forces for the floats of Figures 36d and 36e are 

 shown in Figure 3 7 along with a comparison with theoretical results 

 according to Eq.(34) (except z. was assumed negligible) and with the 

 simplified Newman (or Froude-Krylov) theory which neglects that added 

 mass type force. Model results are corrected to the full-size float in 

 this and all subsequent figures. The effect of rounding of the bottom 

 end of the float is insignificant and cannot be detected within the ac- 

 curacy of the experiments. The phases between the wave and the heave 

 force are not shown in the figures but, in general, for low frequencies 

 the heave force is almost in-phase with the wave (maximum upward in 

 way of a wave crest) while at high frequencies the force is nearly 180° 

 out-of-phase with the wave. It may be noted that the agreement of test 

 results with the complete predictive theory is quite good for this case. 

 A comparison for a fuller float, which had been tested by Mercier [64j 

 on a previous project, is shown in Figure 38. A computation procedure 

 applied by Ochi, [65] based on two-dimensional strip theory is also 

 shown. It is seen that the calculations are not as satisfactory for this 

 rather fat float. 



Tests with the attenuators attached to the upper part of the float 

 through the hinge indicate that the vertical forces due to waves are not 

 affected by the hinge, within the limits of experimental accuracy. 



The side forces measured in waves are exhibited in Figure 39 

 for the full float of Figures 36d and 36e. Again, no influence of the 

 rounded bottom is discernible. The phase of the force is approximately 

 90° with respect to the wave, indicating that the force is predominant- 

 ly due to pressure gradient and inertia forces. The influence of wave 

 amplitude on the forces and on the phase of the forces relative to the 

 wave has been found to be small for the range of wave amplitudes used 

 in the tests (corresponding to 1 . 1 - ft to 10.0-ft, full size). 



Side force due to waves for the slender float of Figure 36c is 

 presented as a function of wave frequency in Figure 40. This infor- 

 mation is presented in Figure 41 for the rigid and flexible cylindrical 

 models of Figures 3 6a,b. Results for all models with the hinge in 

 place are given in Figure 42 and the corresponding angular pitching 



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