Recordings of submarine motion (roll angle) and fluid motions (transverse and longi- 

 tudinal relative flow velocity) illustrated in Figure 2, may be visualized by considering 

 them frequency band-limited random signals continually oscillating above and below an 

 equilibrium level of zero signal . Very often (especially in the case of wave and ship 

 motions), the spectrum of such motions is characterized by a well-defined peak value 

 which is skewed toward lower values of frequency. The area under the spectrum curve 

 is related to mean amplitude values of the motion, and from the theoretical work of 

 Longuett-Higgins (Reference 2) et al, the following relations connecting mean wave 

 amplitude a to the means of the one-third highest (a.) and the one-tenth highest wave 

 amplitudes (a. ) were found: =■ 



TO 



4£_= 1.800 -4r-= 1.416 (6) 



These amplitude relationships were verified on actual wave height data by J . K. A. 

 Watters (Reference 12), who found the following mean wave height relationships H. 

 from a sample of wave records: 



H l H l 



4?- = 1.94 — — = 1.58 (7) 



From these we conclude that wave height values are given approximately by doubling 

 the amplitude values. Finally, since: a = 0.866\/Ethen 



from which we get: 



2a = H = 1.77VT (8) 



H = 2.83 vT (9) 



3 



H 1 =3.60^ (10) 



TO 



11 



