occurred when the trough of the wave was near the propeller plane, and 

 the minimum values of K'p and Kq occurred when the crest of the wave was 

 near the propeller plane. 



The variations of the time-average loads per revolution are also 

 reasonably consistent with trends predicted by a combination of tro- 

 choidal wave theory and the quasi-steady propeller theory of McCarthy 

 (1961). According to trochoidal wave theory, the orbital velocities in 

 the head waves vectorially combine with the propeller speed of advance 

 so that speed into the propeller is a maximum when the crest of the 

 wave is in the propeller plane, and the axial velocity component into 

 the propeller is a minimum when the trough of the wave is in the pro- 

 peller plane. According to simple quasi-steady propeller theory, which 

 should be valid for the low frequency variation of the velocity compo- 

 nents in a wave, the maximum and minimum time-average loads per revolu- 

 tion occur when the speed into the propeller plane is minimum and 

 maximum, respectively. 



T_he maximum absolute values in waves of time-average thrust per 

 blade T^ w^^^ and time-average torque per blade Mxu „.„ , were com- 

 pared with values caluclated by trochoidal wave theory and quasi-steady 

 propeller theory. In these calculations, the spatial average velocity 

 through the propeller disk under the trough of a trochoidal wave was 

 determined using the formulation of McCarthy et al. (1961). This formu- 

 lation does not consider any possible effect of the hull on trochoidal 

 wave velocities. This spatial average velocity and the quasi-steady 

 procedures of McCarthy (1961) were used to calculate the values of 

 Fjj and Mj^ . The comparison with experimental results is as 



follows : 



Experimental Theoretical 



F /F 1.12 1.14 



^.MAX,-^ ^ 



M 1.09 1.11 



^,MAX,? 



This agreement between theory and experiment is considered to be 

 satisfactory and correlates well with the findings of McCarthy et al. 

 (1961) and others as summarized by Tasaki (1975) . The small differences 

 between theory and experiment may be due to the influence of the hull on 

 wave velocity distribution. The effect of the hull may account for the 

 discrepancy between theory and experiment of the relative phase between 

 the maximum mean loads and the wave trough. The measured result showed 

 the phase of the maximum load leads the theoretical result by approxi- 

 mately one-eighth of the wavelength. 



The maximum absolute values of the peak minus time-average loads 

 per revolution Lj^jvy ^ increased by as much as 12 percent of the time- 

 average loads in calm water without hull pitching above the correspond- 

 ing pe_ak minus time- average loads in calm water without hull pitching, 

 ■^MAX~L (see Table 4). Similarly, the maximum values of the first 



20 



