Propeller -Induced Appendage Forces 



4.0 



3.0 



2.0 



1.0 

 0.8 



0.6 



0.4 

 0.3 



0.2 



0.1 



1 



0.2 0.4 0.6 0.8 



Spacing/Propeller Dieuneter 



1.0 



Fig. 36 - Induced force ratio vs spacing ratio for a 

 three -bladed propeller upstream of an appendage, 

 axial measurements, and an appendage angle of 10' 



The hydrofoil appendage will be represented initially as a source distribu- 

 tion in a uniform flow, thereby accounting for the appendage thickness problem. 

 The effect of the velocity field induced by the cascade of propeller blades will 

 be used for determining the lateral crossflow on the foil and the longitudinal 

 velocity field superposed on the oncoming uniform flow, both of which are non- 

 uniform and nonsteady. 



The normal velocity induced at the appendage results in a vorticity distribu- 

 tion on the appendage, and a nonsteady distribution of axially oriented dipoles 

 along the chord line of the appendage is used to cancel the effect of the longitu- 

 dinally induced velocity component. The various hydrodynamic singularities that 

 represent the flow around a propeller blade and the appendage is represented in 

 Fig. 37. The periodic lateral and longitudinal forces acting on the appendage are 

 determined by application of fundamental hydrodynamic theories for the forces 

 acting on singularities in oncoming flows, and illustrations of the derivation of 

 particular force components are presented in the following discussion. 



207 



