Theory of Unsteady Propeller Forces 



VO - vO . 1/0 









-'77J -L 1 



(SR) 



du , 



* 



(SR) 



du 



(67) 



where 



i^u 





''DS - "4" 





)^(v,) d-n^ t*(T,i.u) 



)2^*o 3,*^0 



B^,2 3^1 



du . 

 (SR) (68) 



To compare the performance characteristics of a ship with a propeller and 

 rudder with those of a ship without a propeller, we define the quantities 



'^t('^l'Vi^s) = ml((,^,ri^,s)-ml^(i^,ri^) , ip(77j , u, s ) = 5^(17 ^ , u, s ) - gp" (77^ , u) , 



^lx=^lx-^lx' ^ly=^ly-^ly' ^lz = ^lz-^lz' ^lr = ^lr-Vlr' ^15=^1^-^1^° 



Then, from Eq. (42) we have 



(69) 



a*°(T]i) =--^lim gR°(^i.u) VI + u , a*(77j,s) =^ 1 im i^CTjj.u.s) v^TT^ . (70) 

 V 2 u-»-i V 2 ^j_,_i 



Assuming for simplicity that the pitch of the helical free vortex shed from the 

 propeller is constant radially, and considering that the period of variation of its 

 strength with respect to time s is in, we can set 



Then Eqs. (18) are rewritten as 



(71) 



i, = xl(^,v) Z u[0^(^) + 0(^)v] +^t, 9 = e^(i) + 0(^)v + S^, (72) 



35 



