Propeller -Induced Appendage Forces 

 •035 -, total 



,030- 



.025 



-020- 



^U^ 



,015 - 



,010- 



.005 - 



vorticit 



thickness 



At 



.6 



.8 1.0 



J 



1.2 



1.4 



Fig. 43 - Axial force as a function of the advance ratio for a ■'■! 

 two-bladed propeller: = 0.05, N = 2, to/2c = 0.05 



as the constituent elements due to propeller vorticity and propeller thickness, 

 are seen to be almost exactly the same for these two cases. An examination of 

 the various theoretical expressions shows that the existence and magnitude of a 

 force depend on the product mN. Thus the first-harmonic blade-rate axial force 

 amplitude of a four-bladed propeller should be the same as the second-harmonic 

 amplitude of a two-bladed propeller, with all other parameters being equal (same 

 value of J, /5, propeller thickness, etc.), and this equivalence is exhibited in 

 Figs, 45 and 46. 



The main contributors to the axial force are the terms denoted Xj and X^, 

 where Xj arises from the sources that describe the form of the appendage in a 

 free stream and X^ is due to the dipole that corrects for the axial induced flows. 

 Computations were carried out to determine their separate magnitudes, as well 



219 



