three experimental conditions with hull pitching in waves. The linear 

 superposition accounts for the phase differences between the hull pitch- 

 ing and the waves, and for the differences in amplitudes of pitching 

 and waves for the various experimental conditions. It is assumed in 

 this linear superposition that the increases in loading due to hull 

 pitching and waves are directly proportional to the amplitude of the 

 hull pitching and the amplitude of the waves, respectively. 



From the experiments in calm water with hull pitching (Condition 2 

 in Table 1) the increase in loading due to a unit pitch amplitude is: 



From the experiments in waves without hull pitching (Condition 3 in 

 Table 1) the increase in loading due to a unit wave amplitude is: 



AL_(t )/c = (L ftj - L)/?. 

 «, C A C, C, A 



AL 



Linearly superimposing the above increases in loading due to pitching 

 only and due to waves only, the predicted loads with pitching amplitude 

 ^A*> wave amplitude ^^*, and with the wave leading the pitch by 



($^ - i^)T-^/2-n seconds is 



Figure 18 compares F^^ component loads calculated by this linear 

 superposition procedure with loads measured in waves with hull pitching 

 for the three conditions run, $^ - $^ = 0, $^ - $^ = 180, ^^ - <i-^ = 90 

 degrees. Figure 18 shows that the linear superposition gives a reason- 

 ably good estimate of both the magnitudes and the variations with posi- 

 tion in the pitch and wave cycles of the peak loads, unsteady loads, and 

 time-average loads per revolution. For most conditions the values based 

 on linear superposition are slightly larger than the measured results. 



26 



