Lehman and Kaplan 



"v." '•■" - C * ,,,'" ' i. * ''- ^ 



T 



21 



-=t:?g=3 



«± 



Fig. 37 - Hydrodynamic singularities representing 

 a propeller blade and an appendage 



The problem of a propeller rotating in the vicinity of an appendage is for- 

 mulated in terms of the geometric arrangement indicated in Fig. 38, where the 

 propeller blades are represented as an infinite cascade of finite chord foil sec- 

 tions moving with a velocity V = wR^ in the negative y direction past another 

 finite chord foil section representing the appendage, with the entire system in a 

 uniform free stream velocity u in the x direction. It can be shown that the com- 

 plex velocity on the appendage due to a cascade of concentrated vortices of 

 strength r' on the line x = x,, spaced a distance d apart is given by 



dZ 



iT' 

 2d 



coth -T (Xp + iy^ - X) 



I < 



< i 



208 



