A Vortex Theory for the Maneuvering Ship 



12. Other Sets of Forces Acting on the Body 

 (case of par. 9) 



12.1. Gravity 



The set of forces is 



- 1 ^ ait2 

 ■S - 2 



Y, = ipAU^ l?'^ [(/x-l)0] 



AL ii2 



'S - 2 



1 .,,2 2W gL p -, 



^ P^^ AL {JI ^^-^^ ' 



2W gL 



(1) 



£s -- IpALU^f ^ [(-M^G-^c)^]- 



n, -- lpALU^^§ [(A^G-^c)^] • 



12.2. Friction, Propeller 



Here the thrust T of the propeller ( 1/2) pAuV and the moment about the 

 y-axis is (1/2) pALU^^T. t is the suction coefficient. One has 



Xf^T- = |pAU2 [-C^ + T(l-t)] , 



Yf,T = ■ 



Zf,T = |pAU2 [-C^+ r(l-t)]^, 



£f.T = |pALU2\q, 



12.3. Forces of Inertia J^ for the Body, Forces Due to 

 Potentials ^ and to Pressures p ' ( ^ ) 



The components of the general resultant on the (x, y, z) -axis are: 



(2) 



879 



