Brard 
REPLY TO DISCUSSION 
Roger Brard 
Basstn d'Essats des Carénes 
Parts, France 
Professor Fink has presented a number of examples of great 
interest, but, in general, not connected at least directly with ship 
manoeuvrability problems, that is with the main purpose of my paper. 
For instance, the first case mentioned by Professor Fink is essential- 
ly related to the damping effect of a bilge keel on the rolling motion of 
a ship at zero speed. 
The concept of vortex sheet does not apply in two-dimensional 
motions except in some cases like that of a flat wing in an unsteady 
motion of small amplitude in the direction perpendicular to the veloci- 
ty of the incident flow at infinity (Karman-Sears problem). Vortex 
theory in inviscid fluid does not permit to predict the growing and the 
shedding of vortices in the vicinity of the edge of a flat plat moving in 
a direction perpendicular to its plane. This phenomenon is dependent 
on the viscosity. The theory however applies provided comple- 
mentary conditions be added to precise the mathematical model. The 
considerations developed by Professor Fink could have been the sub- 
ject of a separated paper to this Symposium, 
The case of a lifting surface with separation at the leading 
edge seems to be similar to that of the A wings. I suggest to Pro- 
fessor Fink to compare his method to those used at present by the 
Office National d'Etudes et de Recherches Aérospatiales (ONERA). 
An ONERA-report is quoted if the list of references joint to my paper. 
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