occurred approximately over the angular positions of 1A5 to 230 degrees 

 In the hull pitch cycle shown in Figure 11. This corresponds to the 

 portion of the cycle in which the hull was passing through its equili- 

 brium value from stem-up to stern-down; i.e., near (i|^ - ^l^cy) = 0, ^ <0. 

 This is the same portion of the pitch cycle during which the maximum 

 time-average values per revolution occurred; therefore, the maximum 

 increase in the time-average loads per revolution and the maximum in- 

 crease in the unsteady loads per revolution tend to add (they are in 

 phase relative to the hull pitch) to yield the maximum increase in peak 

 loads. The smallest absolute values of time-average, peak loads, and 

 first harmonic loads occurred near ijj - ^q^ as the hull passed from the 

 stern-down to the stern-up portion of the cycle; i.e., (^ - i>(^) = 0, 



ii <o. 



Figure 12 shows the variation of the ¥^ component with blade 

 angular position for times in the pitching cycle where the minimtim and 

 maximum peak loads occur. The effect of pitching motion is most extreme 

 at blade position angles around 135 degrees, where the maximum blade 

 loading occurs. This explains why the time-average loads and the peak 

 loads occur in phase during the pitching cycle. 



The unsteady loads are important from consideration of fatigue of 

 the propeller blades, and of the hub mechanism for controllable pitch 

 (CP) propellers. Since a ship may operate for an extended period in a 

 rough sea, the effect of the ship motions, such as hull pitching, on 

 unsteady blade loads is significant. The difference between the peak 

 load and the time-average load per revolution is a measure of the un- 

 steady loading. With this difference as a measure of the unsteady load- 

 ing, the results with hull pitching showed that the unsteady hydrodyna- 

 mic loading for the various components increased by 26 to 38 percent 

 above their corresponding values for iJj = ij^^y without hull pitching. 

 This indicates that the effect of ship motions can significantly in- 

 crease the unsteady loading on the blades. 



The difference in the unsteady loading with and without the hull 

 pitching is probably due to an additional relative velocity component 

 arising from the motion of the hull during pitching. As the hull passes 

 through 4; = ^Q]^ the vertical velocity of the hull (and propeller) is a 

 maximum. As the hull goes from stern-up to stern-down through ij; = ^(^, 

 the upward velocity component relative to the propeller plane tends to 

 increase above the values at fixed hull pitch at ii = 'J^cw* This tends 

 to increase the amplitudes of the first harmonic of the tangential 

 velocity, and thereby increase the unsteady loading (and increase the 

 peak loading) . The maximum vertical velocity of the propeller for 

 sinusoidal pitching with ('I'i^iax ~ '^CW^ ~ 1.33 degrees and frequency = 0.8 

 hertz is approximately 0.29 m/s (0.96 f t/s) . This is equivalent to 

 additional tangential and radial velocity component ratios (Vj-/V and 

 Vj-/V, respectively) of 0.082. For ^ fixed at if = 'l^cw (("^tO.yH/V) = 

 0.199 and (Vj-o.7)l/V = 0.145 (from a harmonic analysis of the wake sur- 

 vey data). Therefore, 



14 



