Surface wave data were recorded by the Sonic Surface Scanner in the form of 

 pulses on magnetic tape . Since this method may prove to be a useful way of obtaining 

 wave data in the open ocean whiie submarines are on routine patrol, the theory and 

 method of this technique are reviewed briefly in Appendix A. 



B . Recording Procedure 



The recording procedure was as follows: The REDFIN submerged to 100 feet (keel 

 depth) and attempted to hold this depth under zero ground speed. Recordings of one- 

 half hour duration were made under these conditions at various headings and wave 

 conditions. Test conditions are summarized in Table 1 . Exact headings were difficult 

 to maintain; headings, relative to wave directions, shown in Table 1 are the average 

 values during each run. Each recording was given two numbers for identification. For 

 example, Run 3-1 is the first recording taken on Run 3. Except for surface wave data 

 and in situ pressure fluctuations, each run was recorded on paper tape for visual anal- 

 ysis and monitoring of data recorded at sea, and, also, on magnetic tape for electronic 

 analysis . 



Most surface wave data in Table 1 were obtained by "hindcasting" from synoptic 

 weather maps (Reference 9). There were a few visual observations, but these observa- 

 tions are considered unreliable, limited in many cases by darkness. The general diffi- 

 culties of making visual wave observations at sea are discussed in Reference 11 . Hind- 

 cast wave data provide an independent source of wave height, period, and direction. 

 These are particularly useful as a check on the accuracy of visual observations made 

 aboard a submarine, in the event no surface data are available from the Sonic Surface 

 Scanner . 



III. THEORY AND METHOD OF POWER SPECTRUM ANALYSIS 



A. Spectrum Analysis 



A preliminary analysis of most of the variables discussed in this report was pre- 

 sented in Reference 8. This report contains mean and maximum values of the peak-to- 

 peak roll angles, and peak-to-peak cross-flow velocities. However, motion charac- 

 teristics of such variables (including surface wave motion) can be more completely 

 described by computing energy spectra of the recordings. Analog and digital recordings 

 of motion data described in this report are assumed to be samples from quasi -stationary 

 Gaussian processes whose mean values are zero. Such processes are completely described 

 by their energy (power) spectra . 



Suppose part of a given recording of the process occurs as shown in Figure 3. 

 Although such functions are random, amplitudes of the process (determined from a line 



