318 P. Mandel 
doubtlessly ensue. The natural rolling period of a submerged submarine is conveniently 
expressed as follows: 
Tn = 271kx/V gBG 
where = the natural roll period 
=- radius of gyration of weight about the longitudinal axis of 
symmetry (varies from about 3.3 feet for condition 9 in 
Table 2 to 3.6 feet for conditions 4 and 5) 
g = the acceleration due to gravity 
BG = the metacentric height (tabulated in Table 2). 
=~ 
eae 
Utilizing all of the preceding information, it would be possible to predict which of the 
nonequilibrium conditions shown in Table 2 was likely to result in severe oscillations. How- 
ever, this information would be insufficient to permit an estimate of the amplitude of oscilla- 
tion. Furthermore, a freely rising submarine could obviously partake of coupled motions that 
might render the elementary analysis discussed up to this point inadequate. For these 
reasons the decision was made to conduct an experimental model study of the ascent of the 
Aluminaut. 
MODEL STUDY 
The Model and Facility 
On the basis of a model-scale study conducted by the author, Southwest Research Insti- 
tute constructed the 1/12-scale, 49-inch-long hollow aluminum model shown in Figs. 6 and 
7. The unfairnesses evident in Fig. 6 were ameliorated by the use of modeling clay, and as 
Fig. 6. Assembled aluminaut model 
