Thus a combined theoretical and experimental study is presented 

 with a comparison of the two. The comparison is quite good for the 

 original mine configuration at the short wavelengths (40 feet) where the 

 experiments are reliable. At the longer wavelength (55 feet) there is 

 more scatter of the experimental data, and comparison with the theory is 

 less conclusive. However, the principal deficiency of the theory is its 

 inability to account for the (predominantly viscous) damping near reso- 

 nance, which occurs for the original mine configuration at much longer 

 wavelengths. To illustrate this, the model was altered physically by in- 

 creasing the length of the mooring arm, bringing the resonance frequency 

 into the range of experimental wavelengths. The resulting data near reso- 

 nance is substantially different from the theoretical prediction, so that 

 motions at all wavelengths cannot be accounted for with the theory. 



To provide statistical predictions in a realistic seaway the reso- 

 nance response is determined empirically, using as a rough guide the 

 experimental data with the long mooring arm. The Pierson-Moskowitz 

 spectrum for fully-developed seas is then applied for Sea States 4 through 

 7 and yields predictions of the root-mean-square pitch amplitude for two 

 mines at various depths of submergence. It is significant that, due to 

 different values of the excess buoyancy of the two mines, the resonant 

 frequencies correspond to very different wavelengths (450 and 1340 feet); 

 thus the relative superiority of the two mines depends critically on the 

 sea state and also on the depth of submergence. It is clear from this 

 comparison that small changes in the volume or weight of such a body can 

 have large effects on the motions. 



ANALYTICAL DERIVATION 



In this section we shall derive the equations of motion of a 

 moored, submerged body in regular waves. The following assumptions are 

 made: 



1. The fluid is inviscid and incompressible. 



References are listed on page 22. 



