Therefore, it is concluded that linear superposition of the separate 

 increases in blade loads due to pitching and waves gives a good, or 

 slightly conservative, estimate of net increase in blade loads due to 

 operation in waves with hull pitching. 



In order to evaluate the relative importance of the amplitude of 

 hull pitching, the amplitude of the waves, and the phase difference 

 between the hull pitch and the wave at the propeller, the experimental 

 results with hull pitching in calm water and the experimental results in 

 waves without hull pitching are linearly combined as described previously 

 to simulate blade loads for the following values of ij;^, and ?j\/^PP' 



^. = 1.0 degrees, C /L = 0.01 - representing calm to moderate 



sea conditions 



^. = 2.0 degrees, C./Lpp = 0.03 - representing moderate to rough 



sea conditions 



Figure 19 presents the maximum values of the F^^ component time- 

 average loads per revolution, peak loads per revolution, and the peak 

 minus time-average loads per revolution calculated by linear superposi- 

 tion for the selected values of pitch amplitude and wave amplitude over 

 the complete range of the relative phase between the pitch and the wave. 

 Only the Fx component is shown since the pertinent trends are basically 

 the same for the F^, My, M^j aiid Fy components. The abscissa of these 

 curves, ^c, ~ ^xb* ^^ the phase angle by which the pitch lags the wave at 

 the propeller relative to the frequency of encounter or the pitching 

 frequency. 



The results shown in Figure 19 indicate that for given amplitudes 

 of waves and pitching the maximum values of the time-average loads per 

 revolution, peak loads, and unsteady loads (peak loads minus time- 

 average loads per revolution) vary substantially depending on the dif- 

 ference in phase between the hull pitch and the wave at the propeller, 

 ^l^ - $^. The peak loads are more sensitive to this difference in phase 

 than are the unsteady loads which, in turn, are more sensitive than the 

 time-average loads per revolution. The time-average loads, peak loads, 

 and periodic loads are near their respective largest values in the 

 region where -30 degrees <($r - $^)< 120 degrees; i.e., where the crest 

 of wave reaches the propeller between 120 degrees before and 30 degrees 

 after the maximum stern-up position in the pitch cycle. Over this 

 region of $r - ^\b the maximum increase in loads due to pitching in calm 

 water and the maximum increase in loads due to waves without hull pitch- 

 ing add almost algebraically, i.e., there is very little cancellation 

 due to phase differences between these increases. The values of the 

 maximum peak loads and maximum unsteady loads reach their smallest 

 values near <I>j^ - $,j, = 2A0 degrees. These trends hold true for the Fx, 

 My, Fy and Mx components for all combinations of amplitudes of hull 

 pitching and amplitude of waves which were evaluated. 



In summary, the experiments with hull pitching In regular head 

 waves with pitching frequency equal to the wave frequency of encounter 

 showed the following : 



27 



