Brard 
Let us suppose that the wing is in a uniform motion of trans- 
lation and that the relative motion is steady. Figure 5.3 shows the 
general configuration of the vortex distribution. The free parts of 
the vortices are closed at infinity downstream from the wing. (In the 
figure the concentration of the free vortices around the edges of the 
free vortex sheet is neglected), The second frontier between), and 
>» consists of the bound part of the vortex filament shed at the junc- 
tion of the leading edge with the trailing edge. The sum )/, oe 
does not cover entirely the wing surface) > . The vortices located 
on ee eae ay Pas 5) contain no free arc ; they make closed 
rings entirely located on 3° 
Let som denote the intersection of dr f, With >) a and 43. 
that of >> f, With y e, : These two curves are infinitively close to ‘ 
The relative velocity Vp is tangent to PB, e, at every point 
Ba. end to e> at every point Be, . These two points can be 
2 e2 ; 
considered as belonging to Deice and to a fe respectively. Thus 
VR (Be,) - Viz (B*) and Vig (B*)\- VR (Be,) are equal and orthogonal 
to pee Balt |VR (Be) | = | Vp (Be_) | because the pressure is con- 
: 2 : : 
tinuous through the free vortex sheet as shown in Section 4. Con- 
sequently Vp (B°) = 0. Hence Lf is orthogonal to ‘om ° vend 
also are orthogonal to since they are orthogonal to ve on 
and on Do. respectively. Furthermore the intensities dI, = 
OVER (Bé,) . BB' and di, =.- Vp (Be,) BB' are equal. Hence, as 
shown by Maurice Roy. 
df) V2) adr -— ar (5.24) 
f 
Of course, this relationship does no longer hold when the motion is 
unsteady. 
B - STEADY MOTION IN THE CASE OF SEVERAL SHEDDING 
VORTEX LINES 
One case of several free vortex sheets is sketched in Fig. 5.4 
which represents the lower half of a double model the two halves of 
which are the images of each other with respect to the (X, Y) - 
plane. The (Z, X) - plane is the longitudinal plane of symmetry of 
the hull. The fluid is unbounded. The body is in a uniform motion of 
translation in the positive x-direction and the fluid motion is sup- 
posed to be steady. The drift angle a = (Ox, OX) is positive, so 
that the starboard side is the pressure side and the port side is the 
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