Theory of Unsteady Propeller Forces 

 Then from Eqs. (27), (28), and (69) Eqs. (29) and (30) are rewritten 



1 i Jl - V 



X 7T V 1 + V 



5*0 Bd) 



— + — + v': " + v". 



,* 



. (SP) 



dv 



IVr 



1 



1 fjl- Vl^, 



!)*o B$ 



+ + vT^ + V 



^30 ^dd 



*o + V* 



(SP) 



dv 



K(^'-K)-Ml^KI . ©(0=||\^4^^^^^dv 



© (.o + 



- f 



2772 J 



ds 



1 - V 



1 + V I'o 



6*0 ^('I'H + 'fRC+t'Rt) 



'di 



B- 



,* 

 Ix ' ■ Ix 



+ V , " + V, 



(SP) 



dv ' r ds \^^ 



277 2.- 1 j , V 1 + V 



^ + 



3^*0 ^(^'h+^R +^Rt) 



^B0 



^de 



dv 



J(SP) 



^=/(l+<fB^ )' 



(76) 



By reference to Eqs. (69), (61), and (62), the boundary conditions of Eqs. (32) and 

 (34) are rewritten 



c(^.^l'S) 



+ (-1)""' 



B(I) 



az 



3(D 



34(^i'^i) 



(SH) 



^^1 





^4(^^i-^i) 



(SH) 



Bt]i 



B<I) 



Bt] 



. , (77) 



(SH) 



(SR) ^ (^i) Bu 



B .b 



. 



(78) 



(SR) 



And the boundary condition of Eq. (33) on the propeller blade is rewritten 



BO 30*0 *„ .* ■ 



+ —^ + V + V 



di B^ 1" 1'' 



(SP) 



" B(D B^ 



+ vT" + V- 



le 



-I(SP) " 5(^)^v 



. (79) 



The difference of water pressure between the case of the ship with a propel- 

 ler and rudder and that of the ship without a propeller, which is denoted by Ap*, 

 is expressed from Eqs. (36), (63), and (69) as , 



37 



