the periodic loads. Due to the hull boundary above the propeller, the 

 maximum upward orbital velocity into the propeller is only 50 percent 

 or less of the corresponding upward orbital velocity in an unbounded 

 fluid for ships with high-speed transom sterns and exposed shafts and 

 struts. Therefore, for these ships the maximum periodic blade loads due 

 to waves can be approximated from the corresponding loads without waves 

 as follows : 



'h 



■1AX,C 



0.5 V 



^W7 



0.5 V 



A r 



where At = maximum increase in periodic loads with waves over the 

 ' values in calm water 



L = periodic blade load in calm water 



V = maximum vertical component of the orbital wave velocity 



in the propeller plane neglecting the influence of the 

 hull 



(V ) = first harmonic of the tangential wake at the 0.7 radius 

 in calm water 



V = vertical component of spatial average crossflow velocity 



in propeller plane in calm water 



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 wave cycle. Therefore, the increase in peak loads due 

 to waves is approximately the sum of the increases in these components: 



^^PEAK,? " ^^MAX,C "^ ^^mX,Z 



Figure 17 shows the variations of the higher harmonic amplitudes 

 of the Fjj component of blade load through the wave height cycle. For 

 the case of waves, it appears that the second through fifth harmonic 

 amplitudes show distinct periodic variations up to 50 percent of the 

 calm water values. The sixth through tenth harmonic amplitudes show a 

 more random variation of a lesser extent. This is contrary to the 

 pitching results where less variation occurred over the greater and 

 lesser harmonics and extreme variations occurred in the fifth through 

 eighth harmonics. The large variation in the third, fourth, and fifth 

 harmonic amplitudes of F^^ would lead to significant modulation in the 

 periodic bearing fortes produced by the four-bladed model propeller. 

 The large variation in the second through fourth harmonic amplitudes 



24 



