The theoretical probability distribution would always indicate that a 

 certain value of pitch amplitude [peak value) would be exceeded, even 

 though this probability may be extremely small. In actuality the distri- 

 bution will be truncated at some finite value of pitch amplitude. This 

 cut-off point is not known with any certainty; however, it is reasonable 

 to assign some low value of probability, for instance, . 0001, beyond which 

 no value of pitch motion is considered to exist. 



The probability of exceeding pitch amplitudes of 51 and 60 degrees 

 for various sea states and buoy depths is presented in Tables 4 and 5. 

 These results show that neither body will exceed these angles in Sea State 

 4. As the sea state increases these angles will be exceeded first at the 

 shallow depths and, finally, in Sea State 7 at all depths for which the 

 calculations were made. 



CONCLUSIONS 



1. The theoretical predictions of the pitch motions of the MARK 56 and 

 MARK 57 mines are reliable, except near resonance, which will occur at 

 wavelengths of approximately 450 and 1340 feet, respectively. At resonance 

 the motions are governed by viscous damping which can not be predicted 

 with confidence from theory or experiments. 



2. For wavelengths less than 700 feet the MARK 57 mine is superior with 

 regard to minimization of pitching motions. But for larger wavelengths 

 the MARK 56 is superior and with a larger difference involved. 



3. In a seaway both the relative and absolute performance of the two mines 

 depends on the sea state and the depth of submergence, the MARK 56 being 

 better in situations involving higher sea states and deeper submergence 

 depths . 



14 



