Brard 
behavior of the curves giving the density of the bound vortices in the 
plane of symmetry of the ship (y = 0). Let §& denote the reduced 
abscissa 7 , the origin of the moving axes being at the center of 
the plane y=0. 
The integral equation of the problem expresses that the velo- 
city induced by the total vortex distribution is tangent to the plane 
y = 0. We give below the density f( & ) of the circulation. In the 
case of an oblique translation, one has : 
draft/length ratio, a = drift angle, and 
ree) 
6 
I 
& 
oe 
I 
Str 
+ 
° 
nN 
; 6 = Dirac function 
projection on the plane y = 0 is at the abscissa Ey - — SLA ates 
one has : 
rVL L 
38 = € —— : 
Sad 5 aa a eae 
A OU AD st Deen 8 GEASS) en 
Figures 8.2 and 8.3 show the graphs of ¢ in the first 
case and in the second case respectively. 
The force Y and the moment N with respect to the z-axis 
(vertical upwards) are 
1 Zz ie es 1 
See oe oy Eee eee 
= SV re cos ala sina + Boe rox | (5) 
1 1 Zz ib Telly 
Ni =f? == p6¥ he nests (RAL Le ws =| b 
7.4 1 cosa | sina By = Cc, an lan | Cc, c(s,) 
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