0- Angular variable in cycle of wave encounter, Zirt/Tg; 0^ = 

 when ^ = 0, ^>0 



0^ Angular variable in cycle of hull pitching, Zirt/T^; 0^ = 

 when ii = 0, ^>0 



Angular coordinate used to define location of blade and vari- 

 ation of loads measured from vertical upward; positive clock- 

 wise looking upstream for starboard propeller (righ-hand 

 rotation) , positive counterclockwise looking upstream for 

 port propeller (left-hand rotation) , 9 = - Qy 



e„ Angular coordinate of wake velocity measured from upward 

 vertical; positive counterclockwise looking upstream for 

 starboard propeller (right-hand rotation) , positive clockwise 

 looking upstream for port propeller (left-hand rotation) , 

 6w = - 6 



y Angle between the direction of the waves and the ship 

 centerline 



p Mass density of water 



$j- Phase of wave at the propeller plane based on sine series, 

 C(t) = C^ sin (0^ + $^) 



$^ Phase of hull pitch based on sine series, ^{t) = ^A sin 



(©,); + ^^l,) _, 



(J)(r) Pitch angle of propeller blade section, tan -•- (P/(2irr)) 



i<i>v M)r, nth harmonic phase angles of F,M based on a cosine series, 

 ■''»'^" jg 



(F,M) = (F,M) + Z^ (F.M)n cos (ne - ('f'p^^)^) 



i|) Pitch of hull, positive stern up 

 TpA Amplitude of hull pitch angle 



Subscripts: 



CW Value in calm water 



Exp Experimental value 



H Arising from hydrodynamic loading 



h Value at hub radius 



M Model value 



MAX Maximum value 



MIN Minimum value 



p Port propeller 



PEAK Peak value including variation of both time-average value per 



revolution and variation with blade angular position 



s Starboard propeller 



x,y,z Component in x,y,z direction 



0.7 Value at r = 0.7R 



t, Value for operation in waves 



i|) Value for operation with hull pitching motion 



Superscripts: 



— Time- aver age value per revolution 



Unsteady value, peak value per revolution minus time-average 



value per revolution 



Rate of change with time 



33 



