harmonic loads (L)imay» increased as much as 9 percent of the time- 

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

 ing first harmonic loads in calm water without hull pitching, (L)-j^. The 

 variations of the peak minus time-average loads per revolution and the 

 first harmonic loads approximately followed the local wave elevation in 

 the propeller plane so that their maximum absolute values occurred at 

 approximately 45 degrees of the cycle of encounter before the time at 

 which local wave elevation passes through the calm water level from 

 negative to positive (? = 0, C>0) . 



The variations of the peak minus time-average loads per revolution 

 and first harmonic loads are reasonably consistent with trends predicted 

 by trochoidal wave theory. According to computations by McCarthy et al. 

 (1961) using trochoidal wave theory, the longitudinal components of the 

 orbital velocities are essentially independent of location in the pro- 

 peller disk; therefore, the longitudinal components of orbital veloci- 

 ties do not contribute to the circumferential variations of propeller 

 blade loads. Trochoidal wave theory predicts that the vertical compo- 

 nents of the orbital velocities in the head waves reach their maximum 

 values in the upward direction at the position where ^ = and ?>0. 

 The wake into the propeller disk for the present hull is predominantly 

 an upward velocity due to the inclination of the propeller shaft rela- 

 tive to the hull (see Figure 6); therefore, at C = 0, i>0 the orbital 

 velocity and the wake velocity vectorially combine to produce the maxi- 

 mum upward velocity relative to the propeller, which is equivalent to 

 the maximum first harmonic of the tangential velocity. The first har- 

 monic of the tangential wake is the primary cause of the unsteady blade 

 loads on the present hull operating in calm water without pitching; 

 therefore, the maximum unsteady loads in trochoidal waves should occur 

 at ? = 0, i;>0. The measured results show the phase of the maximum 

 unsteady loads leads the predicted result by approximately one-eighth 

 of a wavelength. 



The ratio of the maximum variation of blade loading with blade 

 angular position in waves to the corresponding variation of blade load- 

 ing in calm water should be proportional to the ratio of the maximum 

 vertical velocity in waves to the corresponding vertical velocity in 

 calm water (since the vertical velocity is proportional to the first 

 harmonic of the tangential component of velocity) . The temporal maxi- 

 mum upward vertical velocity in the propeller plane (this velocity is 

 essentially constant over the propeller disk) in a trochoidal wave 

 corresponding to Condition 3 in Table 1 was calculated using the formu- 

 lation of McCarthy et al. (1961) to be 0.235 m/s (0.772 f t/s) . This is 

 equivalent to an additional tangential velocity ratio V^/V of 0.066, 

 The value of (Vt;0.7)l/V for operation in calm water is 0.199 from the 

 wake survey results. Therefore, 



^^t0.7-'lMAX^^ = 0.199 + 0.066 ^ 

 (\0.7)l/^ " '■^'' ' ' 



21 



