propeller over a range of ship and propeller operating conditions; how- 

 ever, this ratio is not a good parameter for comparing the unsteady 

 loadings on different propellers on different ships with different oper- 

 ating conditions. Analytical calculations, not presented here, confirm 

 that the periodic loading components for operation in calm water with 

 no ship motions should be larger fractions of the respective time-average 

 loading components for the propeller-hull combination described in the 

 present paper than for those described by Boswell et al. (1976a, 1976b, 

 1978). 



E. Operation in Calm Water with Hull Pitching 



Figure 11 shows the variations of peak values per revolution, time- 

 average values per revolution, and first harmonic values of the F^ and 

 Mx components of hydrodynamic blade loading with hull pitch angle ^ 

 (Condition 2 in Table 1) . The Fy and My components showed similar vari- 

 ations as in Figure 11, and the Fz and Mz components were found to be 

 relatively independent of hull pitch, and therefore are not shown. 

 Table 4 summarizes the maximum absolute values of the peak loads, first 

 harmonic loads, and time- average load per revolution for operation in 

 calm water with hull pitching. 



Figure 11 shows the loading components at the individual pitch 

 angles analyzed. Spline curves were fit through the points shown. An 

 oscillatory behavior is shown in the peak and first harmonic loads at 

 the time when the hull is moving from stem-up to stern-down position. 

 This behavior was believed to be caused by observed slight transverse 

 oscillation of the dynamometer boat probably caused by vortex shedding. 

 This did not occur in the experiments described by Boswell et al. (1976a, 

 1976b, 1978) because the djmamometer boat was not completely submerged 

 in those experiments as it was in the present experiments. This be- 

 havior was believed to have no significance, since the model hull did 

 not oscillate transversely in a similar fashion. Therefore, this os- 

 cillation is faired out in the curves shown in Figure 11. 



The time-average values per revolution for each of the two loading 

 components remained within 5 percent of their values in calm water 

 without hull pitching throughout the pitch cycle presented. The trends 

 in variations of the time- average values of the various components with 

 position in the pitch cycle are similar. The largest absolute values 

 of the time-average values per revolution of all loading components 

 occurred near the time at which the hull pitch was passing through its 

 equilibrium value from stern-up to stern-down; i.e., near (ij; - ij^cvj) ~ 

 0, ^ <0. 



The maximum absolute values of the peak loads increased by as much 

 as 22 percent relative to the time-average loads in calm water without 

 hull pitching above the corresponding peak loads in calm water without 

 hull pitching. Similarly, the maximum values of the first harmonic 

 loads increased by as much as 13 percent relative to the time-average 

 loads in calm water without hull pitching. The maximum absolute values 

 of both the peak loads and the first harmonic loads for all components 



13 



