Liehman and Kaplan 



,10 -, 



,08 ■ 



,06 



,04 



f u2wR2 



.02 ■ 



01 -J-Ao 



.05 



.10 



.15 



.20 



Fig. 49 - Blade-rate transverse force as a function of the 

 spacing distance for a three -bladed propeller: J = 1.0, 



3, 



1, t„/2c = 0.10 



forces and odd-bladed propellers produce transverse forces as the fundamental- 

 blade-rate effects on a symmetrical appendage. The existence of a particular 

 force depends upon whether the product (Nm) of the harmonic number and the 

 number of blades is even or odd. 



3. The influence of propeller thickness is significant in determining the total 

 amplitude for both the transverse and axial appendage forces. The force ampli- 

 tudes for a propeller with a particular number of blades are a function of the 

 product Nm, so that higher-harmonic force amplitudes for a propeller will be the 

 same as those for the blade- rate amplitude of a propeller with a larger number 

 of blades but the same Nm. 



4. The axial forces are proportional to the appendage thickness. 



5. All induced forces on an upstream appendage decrease exponentially with 

 an increase in propeller spacing, with a faster decay for the higher harmonics 

 and for an increased number of blades. This decay with distance exhibits no de- 

 pendence on the advance ratio, implying the same decay rate for all advance 

 ratios. 



224 



