A Vortex Theory for the Maneuvering Ship 



Assuming that u/u, v/u , w/L, Lp/u, Lq/u, Lr/U have negligible squares and 

 products and the same for ^q, i^, the general expression of the set of forces of 

 inertia is: 



L^ 



U2 ^G 



L^f 



L^P 



— + Y 



U2 13 u 



L^q 



IT2 



L^r 



— ^ + V 



L^ 



13 ,t2 



y (2) 



In the present case, the motion is parallel to the (z,x) -plane. Then, taking 

 into account the formulae (42), par. 5.4, we have: 



Z„ + Z; 



1 A„2 2W 



Xe + X, . JPAU^I^ 



)1I, + 31I, = |pALU^ ^ 



AL 



Lq , Lw , Lu , L^q 



Lq , Lw , Lu , L^ q 



U , N W . , ^ , Lw 



43 + 2^13 u + (A^3 - A^l) u + (^35 +^^g) -^ 



Lii 



+ (^Is-^^g) Tvy- (^2+/^>^2) 



L^q 



^ (3) 



7.3. Viscous Drag and Propeller 



We assume, for simplification, that the viscous drag may be expressed by a 

 c and a c -coefficient. On the other hand, we assume that the thrust of the 



X m ' 



propeller is T, the suction coefficient t, we neglect the torque due to the 

 propeller. 



221-249 O - 66 - 56 



865 



