Brard 
REPLY TO DISCUSSION 
Roger Brard 
Basstn d'Essats des Carénes 
Parts, France 
I agree with Dr. Breslin that a real ship is not reducible to 
part of a vertical plane and that, for this reason, Casal's model does 
not give the exact features of the flow about a ship. 
I think, however, that many points of Casal's approximate 
solution are of interest. The existence of a concentrated bound vortex 
near the stem seems to me in qualitative agreement with experiments. 
The fact that, in the case of a ship in translatory motion at small 
angle of attack, the lateral force is often located ahead of the stem 
could be explained by the velocity induced on the stern by the strong 
vortex filament to which the said concentrated bound vortex belongs. 
One of the drawbacks of Casal's model is that the boundary 
condition on the hull is satisfied only on a horizontal segment at equal 
distance from the two horizontal edges of the longitudinal plane of 
symmetry. Furthermore the solution does not fulfill the pressure 
continuity condition through the free vortex sheets in the vicinity of 
the shedding lines. 
Iam not so optimistic as Dr. Breslin about thin wing theory 
with an aspect ratio of .2. One of the advantages of Casal's theory is 
that it is an approach for taking into account the fact that the so-called 
trailing edge is a very short part of the true shedding line (often less 
than 20%). 
In conclusion I would like to thank warmly the discussors. 
Their valuable remarks will give me the opportunity to improve in 
some places the initial version of my paper. 
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