displacement effect of the hull above the propeller, the vertical speed 

 of the propeller relative to the local fluid particles is only 60 per- 

 cent or less of the vertical speed of the propeller. Therefore, for 

 ships with high-speed transom sterns with exposed shafts and struts, the 

 maximum periodic blade loads due to hull pitching can be approximated 

 from the corresponding loads without hull pitching as follows: 



AL, 



0.6 V, 



where Al. = maximum increase in periodic loads with hull pitching 

 over the values without ship motions 



L = periodic blade load without ship motions 



V = vertical component of spatial average crossflow velocity 



in propeller plane without ship motions 



V = maximum vertical velocity component of the propeller 



due to the pitching motions 



3. Peak Loads 



The maximum values of the periodic variation of loads with angular 

 position and the time-average loads per angular position occur near the 

 same point in the pitch cycle. Therefore, the increase in peak loads 

 due to hull pitching is approximately the sum of the increases in these 

 components : 



'PEAK,t(^ " '^hiAX,ii "^ ^■^MAX,iJ^ 



The nZ-1, nZ, and nZ+1 harmonics of blade loads directly contribute 

 to the periodic loads on the propeller shaft and bearings. Full scale 

 measurements (Tasaki, 1975) Indicate that the amplitudes of periodic 

 bearing loads are modulated by the influences of a rough sea. The maxi- 

 mum amplitudes of these modulated loads at blade rate frequency are 

 commonly more than a factor of two greater than the corresponding ampli- 

 tudes of the loads measured in a calm sea as- discussed by Lipis (1975) 

 and Tasaki (1975). In the present investigation, the influence of hull 

 pitching on periodic bearing loads was investigated by evaluating the 

 influence of pitching on the pertinent harmonics of blade loads. 



In the investigations described by Boswell et al. (1976a, 1976b, 

 1978) , no analysis was made of the harmonics of blade loads beyond the 

 dominant first harmonic because of their small amplitudes which were, 

 in many cases, around one percent of the time-average thrust (for 

 forces) and torque (for moments). However, for evaluating the effects 

 of waves and pitching on periodic bearing loads, the variations of these 



18 



