Theory of Unsteady Propeller Forces 



where ■ 



K 



xO=-^gl(^.V--\)W\3,^-^ 



d^ d^ 



[v!] 



(SP) 



'rO = -4- gl(<^'V' - ^k)^ 



K.o =^ gi(^.v, -S,) 



3^ ^\sp) 



d^M(?') d0(s^) 



d^ 



d^ 



(SP) 



(SP) 



-^^^-- [V*] 



and Cpp is the section viscous drag coefficient. The section lift coefficient 

 C^l(^' s) of the kth blade can be obtained approximately as . . . ,, 



(51) 



CkL(^-s) = C,L(^'-Sk) 



Similarly as in Eq. (47) we can set the coefficient Cp^ as 



CpD ^ CpDo(^) + ap(^)[C^L(^'S) - bp(^)l' ■ 



/ gi(^,v,-S^)dv 



(52) 



(53) 



where CpoQ(f ), ap(^), and bp(^) are constants to be determined experimentally 

 depending on the section shape and surface roughness. Denoting respectively the 

 thrust and torque of propeller by T and Q, we get 



T = -F^ , Q = M^ . (54) 



Then defining the thrust coefficient Cj and torque coefficent Cq as 



Ct = T/(pn^2D4) , Cq = Q/(pn^2D5) , (55) 



we can obtain from Eqs. (52) and (47) 



v^x ~ ~**I 



^Q - ^Mx ■ 



(56) 



31 



