Theory of Unsteady Propeller Forces 



We denote the Xj, y^, and z^ components of the force by F^^ , F^ , and F^^ re- 

 spectively, we denote the components of the moment about the x , y and z 

 axes by Mp^, M^y, and Mr^ respectively, and then we define the nondimensional 

 coefficients as 



Krfx = FR,/(pn,2D4) , Kppy = FR/(pn^2D4) , Kr^^ = F^^/Cpn^D^) , 



Krmx = M. 



RxAPn^2D5) , Kr^,^ = MR/(pn,2D5) , K^^^ = M^,/(pn^^D^) . (43) 



The total drag coefficient K^p^ is composed of four terms: the term due to the 

 pressure difference between both sides of the mean surface K^, the term due 

 to viscous drag K^^, the term caused by the rudder thickness K^^ , and the term 

 of the suction force at the leading edge Kg. Thus we get 



where 



^RFx ~ ^Di + ^D2 ^ ^D3 ~ ^S 



(44) 



v^ 1 r 



Vr, - 1 ( 



SR) 



d^wC^i) d^(v,) 



dT7j dT7j 



[v.] ^^Jii^'du, 



<^^)J U^i) ^u 





^D3 





1 b[v*1 



r ... , '' (SR) 



VRx(^l-^)d^l J t*(T)j,u) 



du , 



K 



^3 r'" ao(^i'S) 

 s = ^ ^ ^^1 • 



(45) 



in which Cp^ is the section viscous drag coefficient of the rudder. The section 

 lift coefficient Cj^i^(r]^,s) is expressed approximately as 



1 



(46) 



Then we can set the coefficient Cpp in the form 



<^RD = CrDo(^i) + aR(^i)[CRL(^i'S) - bR(^i)J^ • 



(47) 



29 



