6. Although spectra of roll angle and cross-flow velocities were presented with 

 relative heading as parameter, no consistent relationship is Indicated by these spectra 

 data. This is attributed largely to the low sea state values which persisted throughout 

 the test except on Run 3. 



VII . FUTURE TEST AND ANALYSIS PLANS 



1 . Data discussed in this report are representative of lower sea states. To 

 correctly assess the Influence of environmental conditions on submarine motions, 

 additional data are required during State 4 or 5 sea conditions. Such data should 

 be taken under conditions of head seas (0-degrees relative heading), abeam seas 

 (90-degrees), and following seas (180-degrees), In order to study the characteristics 

 of motion at several different relative headings. 



2. This report presents some examples of "auto" spectra, or the resulting 

 transformation when the wave or ship motion record is autocorrelated (correlated 

 with itself). The extension of the concept leads to cross -spectra, or the transforma- 

 tion resulting when simultaneous recordings of two different random processes are 

 cross -correlated (correlated with each other). A random function of time representing 

 a stationary Gaussian process (for example, sea surface wave motion) could be con- 

 sidered the input or forcing function. The output or response function would be sub- 

 marine motion. Now if frequencies exist In the input such that an excitation response 

 analogous to "resonance" is possible in the output, then such a frequency interdepend- 

 ence is clearly displayed by cross-spectrum analysis. Thus, the use of cross-spectrum 

 analysis provides a useful tool in the study of cause and effect relationships between 

 two random processes . 



3. Recent communication's between leading oceanographers indicate that the 

 array of nine sonic scanners may be used to obtain the directional spectrum of the 

 natural seaway under a variety of sea conditions. Such spectra would be estimated 



by cross -spectrum analysis. Sea surface wave motion is a two-dimensional phenomenon, 

 and energy of wind-generated surface waves has been studied as a function of frequency 

 alone (the notable exception being Stereo Wave Observation Project). 



VIII. ACKNOWLEDGEMENTS 



Most of the analog spectra were computed on the David Taylor Model Basin's wave 

 analyzer; digital spectral estimates were provided by the Division of Computation at 

 the Hydrographic Office. The many problems associated with the Sonic Surface Scanner 



43 



