338 P. Mandel 
Serge G. Bindel (Bassin d’Essais des Carenes, Paris) 
I was very interested in the results given by Prof. Mandel, and particularly in those 
concerning the rolling oscillation during vertical ascent; they confirm the results obtained 
in the Paris Model Tank when studying the bathyscaph of the French Navy. 
I should like, however, to make one remark regarding the dynamic stability of such a 
ship during vertical motion. There is a problem for ascent, but there is generally no problem 
when diving. This fact may be due to the presence of the bridge fairwater, which plays a 
nonsymmetrical role in the two directions of the motion, even if, as in the present case, its 
height is not too large. The effect of the fairwater is, in some manner, like this of a longi- 
tudinal fin on the stability on straight course for a surface ship; when diving, the fairwater 
is aft and its effect is favorable; in the contrary, when ascending, the fairwater is fore and 
its effect is unfavorable. The problem is, of course, more complicated than for a surface 
ship, because of the existence of a static positive stability. Therefore, if Karman’s vor- 
tices are responsible for the excitation, my opinion is that it is necessary to take into 
account the dynamic stability of the motion and, when designing such a submarine, to 
avoid, if possible, a too developed bridge fairwater. 
Owen H. Oakley (U.S. Bureau of Ships) 
I couldn’t resist commenting on Mr. Mandel’s excellent paper because he and I were 
involved together in the business of submarine design for a number of years. I would like 
to make only one comment and that with respect to the comparison of the Aluminaut with the 
Trieste. Mr. Mandel noted a ratio of one to ten in the internal volumes of the two craft in 
favor of the Aluminaut, but that is really not quite fair. One thing should have been empha- 
sized more, and that is that the Aluminaut is good for about 15,000 feet of submergence, 
where the Trieste is good for some 37,000 feet. ‘The problem of density of structure required 
for the deeper submergence comes into the matter very strongly, as does the basic difference 
in the means of providing buoyancy. Mr. Tupper covered a point very nicely that I wanted to 
touch upon, namely, what is the critical speed, and I would like to inquire whether an attempt 
was made to estimate this. 
P. Mandel 
Mr. Oakley has pointed out an oversight in the oral presentation of the paper. The fact 
that the Trieste is capable of diving to more than twice the depth of the Aluminaut places 
some very severe constraints on her design that are not nearly as limiting for the Aluminaut. 
I have more amply covered this point in the written text of the paper. 
I have not attempted to predict the critical speed for the Aluminaut. The critical speed 
is extremely sensitive to the magnitude of the hydrodynamic vertical force and moment due 
to asymmetry, designated Z* and M* in Ref. 2. There is no known method of analytically 
predicting this force and moment and attempts to rationalize experimental values have been 
unsuccessful. In any event there is little necessity for accurately predicting the critical 
speed in the case of the Aluminaut since it is intended to place primary reliance on the 
vertical propeller and on the hydrostatic trim system for control in the vertical plane. 
With respect to the oscillations in dive as well as in ascent, the Aluminaut can only 
descend by means of overweight at a very modest speed. As shown in Table 2, the 
