A General Theory for Marine Propellers 



Fig. 2 - Coordinate system and notation 

 When t is zero, we have 



^= p tan 7+ p 6 tan/^Q , 



(21) 



where y is the rake angle and /3q is the blade element pitch angle at radius p. 

 When t is not zero, we have 



^=ptan7+p6?tan /3q - pfit tan 



(22) 



The last term of this equation relates to the fact that the point Q(^,p,6') is mov- 

 ing along a helical line with a pitch angle of /3. From this equation 



^ - p tan 7+ psi9+ p 0' tan 



(23) 



where s = tan /3g - tan /3 and e' - e - ?L\. is the angular coordinate of Q(^,p,i9') 

 at time t . 



If P (X, r,0) is on the lifting surface when t is zero, we have 



X = r tan y + r0 tan /3p , (24) 



where /3p is the blade element pitch angle at radius r. Then 



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