Analyses of Multiple-Float-Supported Platforms in Waves 



The information obtained from the tests of twenty-five variations in 

 the configuration indicated in Tables 1 and 2 have been analyzed and 

 are presented in two different ways. 



The transfer functions, relating waves and motion, are present- 

 ed in Reference 5 in a series of Tables, such as Table 3 given here, 

 as a function of the non-dimensional frequency parameter, w = ai\vV3/g 

 where a> = frequency, V = average displaced volume of the vehicle, 

 and g is the acceleration of gravity. The displaced volume has been 

 arbitrarily selected as a useful measure of size for non-dimensionaliz- 

 ing. These were derived by spectral analysis of the irregular sea mod- 

 el data using methods similar to those described in detail by Dalzell 

 and Yamanouchi Ll 3J . The sampling interval used for data analysis, 

 0.25 sec, was sufficiently low to assure unambiguous spectra, that is, 

 no "aliasing. " 



Only those spectral results for which the answers appear reas- 

 onable are included in the tabulations. Generally, the measure of reas- 

 onableness is taken to be the coherency and it is preferred that this 

 quantity should have a value of 0.8, or greater. In a few cases, and in 

 some frequency ranges, the test results do not give such satisfactory 

 values of coherency and a judgment concerning the adequacy of a sample 

 of data has been made by a subjective interpretation of graphs of am- 

 plitude and phase versus frequency parameters. Examples of this type 

 of graph are shown in Figure 4 for the results of Test Run 002 (the 

 oscillogram for this run is shown in Figure 3). In this case the range 

 of frequencies for which the coherencies may be considered good is 

 rather wide, especially for the wave -heave correlation. 



In Figure 4 and in the tables, the phase angles are positive when 

 the motion lags the passage of the wave trough by the craft's center- 

 of-gravity. Positive vehicle motions are taken as : surge forward, 

 heave downwards, sway to starboard, pitch bow-up, roll starboard 

 down and yaw bow to starboard, while the maximum positive wave el- 

 evation corresponds to a wave trough. Beam seas tests were conduct- 

 ed with waves approaching the craft from the starboard side while head 

 seas tests, of course, have waves approaching from the bow. 



The non-dimensional angular motion is presented as the ratio 

 of motion (pitch or roll) to the maximum wave slope, as expressed by 

 linear wave theory, w s/g. This is felt to offer some advantage in 

 interpolating the transfer function data for low frequencies - it being 

 realized that for zero frequency (static conditions) the craft must as- 

 sume the slope of the wave, and the amplitude ratio must then be unity. 

 The phase of this motion is, however, reckoned relative to the wave 

 amplitude measurement, and must correspond to +90° (i.e., phase 



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