326 P. Mandel 
pumped out at moderately shallow depths (condition 7), it would take approximately 62.5 
minutes to reach the surface. In fact, better time would be made if no ballast were dropped, 
but full power were preserved and utilized for the ascent using a 30-degree up angle. With 
this assumption it would take only 49 minutes to reach the surface. It appears very likely 
that this method of ascending will be preferred in the normal situation to dropping and losing 
expensive shot ballast. 
Full-Scale Oscillation 
Predicted excitation and oscillation periods for the full-scale Aluminaut are shown in 
Fig. 12. Bearing in mind the results of the model tests, it might be surmised that normal 
ascent conditions 6 and 7A might suffer the most severe oscillations of any of the condi- 
tions. This conclusion is tempered by the fact that, as noted in the previous section, it is 
very likely that propulsion would be used to speed the ascent in these conditions. With the 
boat driven to the surface with, say, a 30-degree up angle, it is not likely that severe oscil- 
lations would ensue even if the shot ballast was also dropped. 
While it is likely that propulsion will be utilized for normal ascents, in the panic condi- 
tions, 8 and 9, propulsion may not be available. Therefore, it is of particular significance 
that these two conditions are, in fact, very far removed from resonance (tuning factor = 5 
and 6 respectively). Therefore, in spite of their low metacentric heights, these conditions 
should not suffer large roll amplitudes. 
Although not noted in Fig. 12, the range of predicted excitation periods on that figure 
is bounded by two different water temperatures. For the full scale, the influence of the 
range of possible values of water kinematic viscosity on ascent velocity and frequency of 
excitation is much more pronounced than the influence of assumed maximum body width. 
Since water temperatures between 40° and 80°F might be encountered, kinematic viscosities 
associated with these temperatures were used to form the boundary conditions. 
CONCLUSIONS FROM VERTICAL ASCENT TESTS AND COMPUTATIONS 
1. Despite large scatter, the experimental drag and oscillation data reasonably conform 
to analytically predicted results. 
2. At resonance a substantial reduction in roll amplitudes can be achieved with wide 
bilge keels at the expense of a considerable increase in drag. 
3. Strong cross-coupling caused the model to attain some ahead velocity. ‘Pitch and 
yaw also were evident during many of the tests. These did not appear to interfere with the 
predicted roll oscillations. 
4. For the normal ascent, the vertical velocity achievable by dropping ballast is so 
low that power preserved and utilized for propulsion would provide larger ascent velocities. 
5. The only two buoyancy conditions liable to experience large roll oscillations are the 
normal ascent conditions 6 and 7A. This situation is vitiated by the fact that in actual 
operation it will probably be preferable to utilize propulsion for the normal ascent rather 
than drop ballast. 
