Lehman and Kaplan 



10. 

 8. 



6.0 



rH 3 



2.0 



1.0 



0.8 

 0.6 



0.4 

 0.3 



0.2 



y./ 



'J -ic 



0.57 K„ 



J 



X 



o J ■= 0.67 K^ » 0.191 

 All 1st Harmonic Conditions 



0.232 



0.2 0.4 0.6 0.8 



Spacing/Propeller Diiumeter 



1.0 



Fig. 35 - Induced force ratio vs spacing ratio for a 

 three-bladed propeller upstream of an appendage, 

 transverse measurements, and an appendage angle 

 of 10» 



The propeller blade will be represented by a vortex distribution, and an in- 

 finite cascade of propeller blades will be considered to pass the appendage, 

 thereby introducing periodicity effects. In addition to the vortex representation 

 the thickness of the propeller blades will be represented by a source distribu- 

 tion. Similar concepts of cascade theory will be used for this source distribu- 

 tion, in the same manner as for the vortex representation. This inclusion of 

 propeller thickness will allow a relative separation of the force effects on the 

 appendage due to the propeller thrust and due to the pressure field arising from 

 the propeller thickness effects. Neither propeller thickness nor periodicity ef- 

 fects have been considered in any of the previous theoretical studies of propeller- 

 appendage interaction. 



206 



