Theory of Unsteady Propeller Forces 



(36) 



In this equation the pressure near the hull is equal to that due to Bernoulli's 

 theorem because of the absence of viscous velocity, and the pressure in the wake 

 behind the hull is considered to be independent of the viscous velocity when the 

 potential flow is negligibly small, because p^ is almost constant according to the 

 boundary layer and wake theory. However, strictly speaking, this pressure p^ is 

 not always a constant independent of time and position. Using Eq. (36) we can 

 calculate the pressure on the surfaces of the hull, rudder, and propeller and, 

 consequently, the forces and moments acting on the hull, rudder, and propeller. 



We first consider the force and moment acting on the hull (8). Denoting for 

 the Xj, Yj, and z^ directions the components of the force due to pressure by 

 ^Hxo' ^H 0' ^^^ ^Hzo respectively, denoting the components of the moment due to 

 pressure about the x^, y^, and z^ axes by M^^^, M^y^, and M^^g respectively, 

 defining nondimensional coefficients as 



^HFxo 



FHxo/(^"r'D^) ' KHpy„ = FHy„/(pn,2D^) , Khp-,, = FH,„/(pn^2D4) , 



KhMxO = %xo/(^"r'D^) . KH^yo -' Vo/(^"r'D^) , Khm.o = ^mo/(p^'^') ' (37) 



where 



n^ = n/2rr (38) 



(revolutions per imit time) and D = 2rQ (diameter), the nondimensional coeffi- 

 cients are expressed as follows: 



?6('^l ) 



^HFxO 





SH) 



+ ^i^mK(^i-^i'S)/Bsld7]^ , 



^HFyO 



"■HFzO 



iA 2 P'^'^^^K 



(SH) 



d^l . 





K=l ^b(^l) 



+ (:ir-iz*(4i,T7j)Bm*(^l,77j,s)/Bs 



drjj 



(39) 

 (Cont) 



27 



