Opttmum Shapes of Bodtes tn Free Surface Flows 
to unknown position of the separation points. Suppose we start with 
K = 0 (K being defined as the ratio of the wetted arc-length to the chord 
length minus 1, or K = s/£ -1), then we know that at K=0, the 
two end points of the cavity boundary would be of the type of fixed de- 
tachment, at which point the curvature of the free streamline is sin- 
gular. As K is increased by giving more arc-length to the body pro- 
file, we hope the profile can be expanded in such a way as to arrive 
at the required optimum shape. When K reaches a certain positive 
value, one of the end points of the optimum profile would firts reach 
the state of smooth detachment (in the sense that the local curvature 
of the free streamline will be equal to that of the body at the detach- 
ment). Near this critical point (K = K, say) and from then on 
(K>K,) I think other physical quantities such as the viscous effects 
and the physical condition,that the pressure on the body remains now- 
here less than the cavity pressure, must be thoroughly examined from 
the final results predicted by the theory. This proposed procedure is 
to be carried out in the future study. Would this answer Dr. Morgan's 
question ? 
DISCUSSION 
Vsevolod V. Rogdestvensky 
Shtpbutldtng Instttute 
Lentngrad, U.S.S.R. 
I think you have done very interesting work, but there are 
many questions in this problem, In order to decide the problem in ge- 
neral, it is necessary to make good tests. I should like to ask, have 
you any comparison with experience ? Have you any experimental 
data ? 
EV29 
