Theory of Unsteady Propeller Forces 



1.0 



OS 



% 



Fig. Z - Longitudinal component of a 

 given inflow velocity . , 



Kfxi(Ji) = m'Kf^2(J2) 



Ji/m ■ 



(138) 



From Eqs. (138) we can calculate ^i or Jj of propeller Mj for a given value of Jj 

 of propeller Mj. Thus we get the ratios of the bearing forces of propeller Mj to 

 those of propeller Mj as follows: 



'Fy 



'•Fy2 



(J2) 



Kyl(Jl) 



(J2) 



K.i(Ji) 



^^Kmx2(J2) 

 ^mxlCJl ) 



^My 





M^Km,2(J2) 

 ^Mzl(Jl) 



AR 



Fx 



ARv 



M^^K^X2(J2) 



AKf,i(Ji) 

 AKmxi(Ji) 



AR 



Fy 



AR 



My 



Fy2 



(J2) 



AKFyx(Ji) 



m'aKm,2(J2) 



'■My2' 



AKMyl(Jl) 



AR, 



AR 



Mz 



m'AKf^3(J,) 



AKfzi(Ji) 



AKm.i(Ji) 



(139) 



First let us calculate the bearing forces of the parent propeller M. The 

 values of the bearing forces Kp-^, K^y, Kp^, K^,^, K^,y, and K^,^ for J =0.70, 

 0.85, 1.00, and 1.15 are periodic functions of period 27r/N = 77/2 and areshown 

 in Fig. 3. The mean values of the bearing forces Kp^, Kpy, Kp^, K|y^, K,^ , and 

 K^jj, and the magnitudes of the vibrating parts of the bearing forces AK^^^, AKp , 

 AKp^, AK^,^, AK^^y, and AK^,^ are presented in Table 4, in which the values of their 

 components caused by viscous drag are shown in parentheses. As shown in 

 Table 4, the ratios of components caused by viscous drag to the total bearing 

 forces are 10% at most. The mean values of the bearing forces and the magni- 

 tudes of the vibrating parts of the bearing forces versus J are shown in Fig,_4 

 and Fig. 5 respectively. From Figs. 4 and 5 the absolute values of Kp^ and K,^^ 

 decrease with increase of J, and the absolute values of Kpy, Kp^, K,^ , K,^^, 



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