^\o.7^1 "*" % ^ 0.199 + 0.082 ^ 

 (V^^ ,), 0.199 ^'^^ 



tO.7'1 



and 



(V ) + V 



'■ rO.7^1 > _ 0.145 + 0.082 _ 



<'r0.7>l ■ °-"5 



These maxima occur at 0^ = 180 degrees which essentially agrees with the 

 value of 0^ at which the maximum loads were measured. The measured 

 increase in unsteady loads arising from hull pitching was somewhat 

 smaller than these calculated increases in tangential and radial veloc- 

 ity component ratios, for example: 



F 

 ^SlAX,4) ^ 0.89 

 F - F 0.72 

 'SlAX ^ 



= 1.24 



Theoretically, the increase in unsteady loading should be approximately 

 proportional to the increases in tangential and radial velocity compo- 

 nent ratios; however as shown by Boswell et al. (1981) including calcu- 

 lations in the authors' closure to this paper, the tangential velocity 

 component appears to have a greater influence on periodic blade loads 

 than does the radial velocity component. This simple analysis provides 

 an upper bound to the dynamic pitching load, since the hull boundary 

 above the propeller would tend to reduce the dynamic pitching- induced, 

 upward velocity component relative to the propeller. 



Other aspects of the data show the influence of the hull boundary 

 on the upward velocity component relative to the propeller. Figure 13 

 shows the propeller plane and hull configuration. It is clear that an 

 upward vertical fluid speed relative to the propeller due to pitching 

 would be minimum near the hull centerline corresponding to a blade 

 position angle of 270 degrees. The vertical fluid speed due to pitch- 

 ing would be a maximum at a blade position angle of 90 degrees where it 

 is close to the edge of the hull. Also, some outward turning of the 

 flow would be expected in this region as the hull moves downward into 

 the fluid. 



This general character of the flow is represented qualitatively in 

 the effect of pitching on the blade load variation with angular posi- 

 tion, shown in Figure 12. As discussed earlier, the effect of pitching 

 is greatest at the outboard blade positions around 100 degrees, where 

 the vertical velocity component due to pitching is greatest. At the 

 inboard positions around 270 degrees, the blade loading is little af- 

 fected by the pitching motion since the hull boundary restricts the 

 relative vertical velocity. Also shown is a phase shift in the peak 



15 



