with 



A Vortex Theory for the Maneuvering Ship 



•^ "^ ^ m 



(6) 



(7) 



%,^^^ -- - h \\ ^01 



(m) 3 T-. dS(m) . 



^ ' dn„ mM 



Functions y^^ii^') and y^^i^') are solutions of the same Fredholm's equation 

 of the 2nd kind, with a right member equal to Ux(m. ) + Cg for y^^ , and to 



Uz(m.)+Ci for 7oi- 



The potentials ^oq.^q ^ may be regarded as generated by bound vortices t^g 

 and tgj. The rings on which the vortices too are lying are the curves >oo = 

 constant. If da^^ is the distance between two rings 7oo = constant, da^ being 

 positive downstream, ip^ the unit vector tangent to S and normal to the ring, i^g 

 the unit vector tangent to the ring, with i^g = nAigg, one has 



t„nS = nAi 



. , ^^0( 



00 Ar^' 



A similar formula gives the vortex tg j . 



3.3. Case When the Angular Velocity is not Equal to Zero (Fig. 3) 



Let us assume now that u/u = , w/u - 0, Lq/U ^ . 



The absolute velocity potential is 



$g(M) = -DgoCM) + ^02 -^ • ^^^" ^ "-^ ^" "e • 



(8) 



(9) 



Figure 3 



825 



