These two response functions are plotted in Figure 7, along with 



-Kh 

 values of the exponential function e for various depths. Also shown 



by dashed lines are approximate expected values for the response near 

 resonance, as inferred from the experiments with the altered (long mooring 

 arm) model. Figure 8 shows the comparison of theoretical and experi- 

 mental data for the MARK 56 mine and for the altered (long mooring arm) 

 version of this mine. The agreement is generally good except for ex- 

 cessive scatter of the experimental data at the longest wavelength, which 

 is attributed to the limitations of the wavemaker and for the breakdown 

 of the theory in the resonance domain of the altered model. 



PREDICTED PITCHING MOTION IN A SEAWAY 



Predictions have been made of the pitching motions of both mines 

 in several idealized sea conditions and at several mooring depths by 

 applying the principles of linear superposition. Using this procedure, 

 the spectrum of pitching motion is obtained by multiplying the wave-height 

 spectrum by the square of the amplitude response in pitch. The form of 

 the wave spectrum used in these calculations is that proposed by Pierson 

 and Moskowitz for a fully developed wind generated sea and is given by 



, , 8.10 x 10-2g2e-°-^4 (V.)4 



where g is the acceleration due to gravity; w = g/V, where V is the wind 

 velocity 19.5 meters above the sea surface. 



The calculations were made for Sea States 4 through 7, correspond- 

 ing to significant wave heights of 6, 10, 15, and 30 feet, respectively. 



These theoretical predictions differ from the above formulae insofar 

 as the fluid density of fresh water is used; the only significant effect 

 is on the cable tension. The theoretical prediction for the long arm is 

 based upon the coupled equations of motion, the pitch amplitude being 

 given by Equation [26]; in this instance, the ratio of %lc was sufficiently 

 large (0.157) to affect the motions. 



12 



