quantities with wave and pitching parameters are more important than the 

 actual values of the small, pertinent higher harmonics of blade loads. 

 Figure 14 shows the variations of the first 10 harmonics of the F 

 component of blade loading with location through one pitch cycle. The 

 value of each harmonic amplitude is nondimensionalized on its calm water 

 value. The variations of the amplitudes of the second, third and fourth 

 harmonic are similar in magnitude to the dominant first harmonic of 

 blade loading. These components are the major contributors to the blade 

 loading variation with blade angle, as shown in Figure 9. The ampli- 

 tudes of the fifth through the eighth harmonics show much larger varia- 

 tions with pitch angle relative to the respective time-average values. 

 This result implies that the relatively small, higher harmonics of blade 

 loading associated with unsteady bearing forces, are very sensitive to 

 relatively small changes in the wake pattern. 



F. Operation in Waves Without Hull Pitching 



Figure 15 presents the variations of the peak values per revolution, 

 time-average values per revolution, and the first harmonic values of the 

 Fjj and Mjj components of hydrodynamic blade loading with wave height for 

 operation in waves without hull pitching (Condition 3 in Table 1) . The 

 Fy and My components showed similar variations as in Figure 15, and the 

 Fz and M2 components were found to be relatively independent of wave 

 height. Table 5 summarizes the maximum absolute values of the peak 

 loads, first harmonic loads, and time-average loads per revolution for 

 operation in waves without hull pitching. 



The maximum absolute values of the time-average loads per revolution 

 ^MAX C increased by as much as 14 percent above the^ corresponding time- 

 average loads in calm water without hull pitching Lj,j^. This is quite 

 different from the corresponding result with hull pitching in calm water 

 where the time-average loads per revolution increased by a maximum of 

 only 5 percent above the corresponding time-average loads in calm water 

 without hull pitching. The variations of the time-average loads per 

 revolution approximately followed the local wave elevation in the pro- 

 peller plane so that the maximum and minimum time-average loads per 

 revolution occurred at approximately 36 degrees of the wave cycle of 

 encounter before the time at which the wave trough and peak, respective- 

 ly, were in the propeller plane. 



The variations of the time-average loads per revolution with posi- 

 tion in the wave are consistent with trends reported by McCarthy et al. 

 (1961). McCarthy et al. measured the low frequency variation of pro- 

 peller shaft thrust and torque with position in the wave for steady 

 ahead operation in regular head waves without ship motions and without 

 a nearby hull. They did not measure individual blade loads; however, 

 the variations of low frequency shaft thrust and torque are essentially 

 the same as the variations of the_time-average values per revolution of 

 blade thrust Fx and blade torque M^. The results of McCarthy et al. 

 agreed with the results of the present^ investigation in that th£ maxi- 

 mum values of the thrust coefficient K-j and torque coefficient Kq 



19 



