295 



THICKNESS CONTRIBUTION 



OOWNSTREAM ■ 



FIGURE 14. Variation of blade frequency verti- 

 cal velocities induced by 3-bladed DTNSRDC 

 propeller 4118 at r = 1.5R and 4> = 0. 



1 

 C2 



= - Jin 



2[l+\Jl-5^] 



- 1 



(1-262) J1..52 



(68) 



and by a suitable coordinate transformation from 

 (M,;;) to (x,r), the velocity V %„ ^^"^ ^^ calculated 

 at an arbitrary point on the propeller blades. 



In general the propeller dipole strength repre- 

 senting blade loading is a function of blade position 

 e (t) , i.e., Ap = Ap(p ,a+e (t) ) . However, in the 

 present experiments the inflow to the propeller is 

 uniform so that the loading is steady and Ap = Ap 

 (p,a). The blades of propellers 4118 and 4119 

 employ NACA a = 0.8 meanline sections. For this 

 section, and assuming a radially elliptical distri- 

 bution of bound circulation, the pressure jump 

 across the blade is given by 



8T 



^0 - \, , 



Ap(p,a) 



in which 



0.9(ai- a„) TT(R 2 - R '^)N 

 I o H 



F(a) (69) 



F(a) = S 



a -a 

 t 



^ ^V^ 



a £0^:0. 8a +0.2 a„ 

 I t I 



0.8 a + 0.2 a ;S a i a (70) 



and T is the steady propeller thrust. 



The calculated values of the forces produced on 

 the spheroid for conditions corresponding to those 

 in the experiment are summarized in Table 4 showing 

 the separate contributions arising from blade loading 

 and thickness as well as the total forces. The 

 latter are also displayed in Figures 9 and 11 and 

 agree quite well with the measurements. 



Additional parametric calculations were performed 

 to study the effect of propeller location on the 

 force produced on an ellipsoid arising from propeller 

 mean loading and thickness. In Figure 15 the 

 attenuation in force (amplitude) with increasing 

 tip clearance is illustrated. (The phase was found 

 to be essentially independent of tip clearance) . 

 Calculations are presented in Figure 16 for a series 

 of axial positions of the propeller with the tip 

 clearance held fixed. As the propeller is moved 

 aft from the nose of the body, the force increases 



TABLE 4. FORCE CALCULATIONS USING METHOD OF VORUS (1974) 



