Oscillating -bladed Propellers 



( T MS • ♦ m. ) 



Fig. 1 - Definitions 



v[, 



sin (7 sin 



The variations of V^ with cp are sinusoidal. For a noninfinite hub, a cor- 

 recting factor of 1/2 may be applied [3j and the tangential component of the 

 velocity be written as: 



1 + 



sin d sin cp = W sin 



This tangential component is to be added to the relative velocity due to the 

 rotation of the propeller n in order to have the angle of attack of the blade ele- 

 ment during its rotation. Supposing that the induced velocities (u^, uj are 

 constant, the maximum variations a^ and a^ of the angle of attack are then 

 given by: 



1 + 



tg a = tgi 



1 + 



J cos 6 1 J cos 6 



± tf 



1 + 



(with the sign - for a, and + for a^). Here x = r/R is the reduced radius (R = 

 D/2 is the radius of the propeller), xj^ is the reduced hub radius and J = V/nD 

 the advance ratio of the propeller. Figures 2a through 2d give the variations 

 of a^ and ttj for two values of x^ and two values of &. 



For a given J , a^ and a2 decrease rapidly with x, i.e., the sections near 

 the hub are more subject to premature cavitation than the outer sections of the 



1499 



