Blade loads were measured for only one amplitude of pitching. How- 

 ever, the maximum speed due to pitching is directly proportional to 

 pitching amplitude for a given frequency; therefore, the peak and un- 

 steady blade loading tends to increase as the amplitude of pitching in- 

 creases. At large amplitudes of pitch the propeller may draw air near 

 the stem-up position. This would tend to unload the blade in the upper 

 portion of the propeller disk so that the unsteady blade loads would 

 increase but the peak loads would not increase. However, this is not 

 the portion of the pitch cycle at which the maximum vertical velocity of 

 the propeller occurs, therefore it appears that maximum steady loads 

 would be controlled by the maximum vertical velocity of the propeller 

 rather than by the air drawing. 



Based on these results and those presented by Boswell et al. (1976a, 

 1976b, 1978), the increase in blade loads due to hull pitching can be 

 estimated for transom stern configurations as follows: 



1. Time-Average Loads Per Propeller Revolution 



Hull pitching increases the maximum time-average loads per revolu- 

 tion by only a small amount over the time-average loads per revolution 

 without hull pitching. This increase can be approximated as follows: 



where AL = maximum increase in time- aver age loads per revolution 

 '^ with hull pitching over the value in calm water 



L = time-average load in calm water 



L, = time-average load in waves 



ill = amplitude of the variation in hull pitch angle in 



radians 



In practice, this maximum increase in time-average loads per revolution 

 due to pitching is negligible relative to the corresponding increase due 

 to waves, as discussed later. 



2. Periodic Loads 



Hull pitching (in calm water) substantially increases the maximum 

 periodic blade loads over the corresponding periodic loads without hull 

 pitching. The primary controlling parameter is the ratio of the verti- 

 cal velocity of the propeller resulting from the hull pitching to the 

 ship speed. The maximum periodic loads occur when the velocity of the 

 propeller and stern are maximum downward. This downward velocity of the 

 propeller effectively increases the inclination of the inflow relative 

 to the propeller and thereby increases the periodic loads. Due to the 



17 



