Breslin, Savitsky, and Tsakonas 



where 77(1) is the time history of surface wave profile measured by the wave 

 probe forward of the model. Figure 5 shows the results of the prediction of 

 heave and pitch response to irregular seas. The continuous lines are tracings 

 of the oscillograph records of heave motion and pitch motion obtained from the 

 tests in Ref. 3. The circled points represent the results of convolving the im- 

 pulsive responses of Figs. 3 and 4 with the surface wave time history. On the 

 whole, agreement between observed and predicted responses is considered ex- 

 cellent, hence validating the accuracy of the impulsive response technique in 

 obtaining deterministic solutions. 



Submerged Bodies in Beam Seas 



The Davidson Laboratory has conducted an extensive series of model tests 

 to determine the motions of a submerged, asymmetrically finned body at zero 

 velocity when acted upon by regular and irregular long-crested waves approach- 

 ing the body from various directions. In these tests, the motions of the sub- 

 merged body were recorded in terms of the surface wave profile directly above 

 the body. Response operators for heave, roll, and pitch motion in beam seas 

 and head seas have been developed from these data by Savitsky and Lueders [5]. 

 The response operators obtained from irregular wave tests were found to be in 

 agreement with those obtained from tests in regular waves. The general con- 

 clusion of this study was that, in regular beam seas, the heave and sway motions 

 are those of a water particle at the center of gravity of the body. Also, in beam 

 seas, the hydrodynamic roll moment is proportional to the wave slope at depth, 

 (or equivalently to the inertia forces which vary as w^) and the roll motions are 

 determined by using this wave slope, the natural roll frequency and damping of 

 the body, and the usual dynamical equations of motion of a linear, single degree 

 of freedom oscillator. 



Dalzell used the results of Ref. 5 to determine the impulsive response func- 

 tion of the submerged body and to calculate the time history of heave and roll 

 motions in irregular beam seas. Dalzell' s results are rederived below following 

 the theoretical procedures described in the previous section of this paper. It 

 will be recalled that, in the present theoretical development, the kernel function 

 of the wave system (due to shift of wave reference points) was separately de- 

 veloped and then combined with the kernel function of the mechanical system to 

 derive a so-called "system" impulsive response function. 



Since the test body was submerged, the wave characteristics at depth of 

 submergence (0, will be used as the input to the system. (It has been shown in 

 the theoretical section that it is equivalent to referencing the output to the wave 

 on the surface.) The relation between the measured regular surface wave pro- 

 file and the orbital motions at depth exhibits a zero phase shift and an attenua- 

 tion in amplitude of orbital motion given by the relation e'^^^Vg. The kernel 

 function relating surface wave profile to wave profile at depth is given in Eq. 

 (56) which is reproduced below: 



Kw(t;o,0 - fYf^e 



480 



