in first harmonic phase shown in Figure 15 indicates a significant 

 change in vertical flow direction due to the hull. 



Blade loads were measured in regular head waves at only one wave 

 amplitude and wavelength. The experiments showed that the increases in 

 both the time-average loads per revolution and the unsteady loads due to 

 waves appears to be controlled by the orbital velocity in a trochoidal 

 wave. It appears that the increase in both the time-average loads per 

 revolution and the unsteady loads are proportional to the orbital veloc- 

 ity. The orbital velocity, and thus the approximate increase in loads, 

 is directly proportional to the wave height and inversely proportional 

 to the square root of the wavelength (Lewis, 1967, McCarthy et al. , 

 1961), neglecting any possible influence of the hull on these trends. 



The vertical component of the orbital velocity, which controls the 

 increase in unsteady blade loading due to waves, is independent of the 

 direction of the waves relative to the ship heading. Therefore, the 

 increase in unsteady blade loading due to waves is essentially inde- 

 pendent of the relative direction of the waves. The component of the 

 orbital velocity in the direction of the ship velocity, which controls 

 the increase in the time- average loads per revolution due to waves, is 

 proportional to the cosine of y, the angle between the direction of the 

 waves and the ship heading. Therefore, the increase in the time- 

 average loads per revolution is essentially proportional to cos y, 

 neglecting any possible influence of the hull on these trends. 



Based on these results the increases in blade loads due to waves 

 can be estimated for transom-stern configurations as follows: 



1. Time-Average Loads Per Revolution 



Waves (without ship motions) substantially increase the maximum 

 time-average loads per revolution over the corresponding time-average 

 loads in calm water. The primary controlling parameter is the change 

 in effective advance coefficient due to the longitudinal component of 

 orbital wave velocity. The hull boundary above the propeller does not 

 appear to significantly influence the longitudinal component of orbital 

 wave velocity. Therefore, the maximum increase in time-average loads 

 per propeller revolution due to waves can be adequately predicted by 

 the use of the trochoidal wave theory neglecting the influence of the 

 hull on the waves, and simple quasi-steady propeller theory using the 

 open-water characteristics of the propeller. 



2. Periodic Loads 



Waves (without ship motions) substantially increase the maximum 

 periodic blade loads over the corresponding periodic loads in calm 

 water. The primary controlling parameter is the ratio of the vertical 

 component of the orbital wave velocity in the propeller plane to the 

 ship speed. The maximum periodic loads occur when the vertical compo- 

 nent of the orbital wave velocity in the propeller plane is maximum 

 upward. This upward orbital velocity component effectively increases 

 the inclination of the inflow to the propeller and thereby increases 



2 3 



