Deep-Diving Submarine Hydrodynamics 323 
Also shown are computed data for the same configurations utilizing data given in Fig. 5 and 
Table 4. The scatter of experimental results is large, but considering the uncertainty intro- 
duced by the presence of an unaccountable amount of flooding water during some of the 
tests, the experimental results were considered as roughly confirming the computed data. 
In particular, the wide keel tests of 6/10-12/59 showed consistent serious deviation from 
the computed data. It will be noted that in none of the tests did the velocities approach 
those associated with the sharp discontinuity in the drag curve. 
Model Oscillations 
Test results of roll oscillation are plotted in Fig. 10 as a function of both ascent 
velocity, determined experimentally, and natural roll period, as tabulated in Table 3. Maxi- 
mum double amplitude rolls observed during each test are shown symbolically for each point 
plotted. Also shown in Fig. 10 are the approximate periods of the roll excitation caused by 
the periodic vortex shedding computed on the basis of the Strouhal number curve shown in 
Fig. 5. With the introduction of bilge keels located at the maximum beam of the model, the 
maximum width to be used in the computation of the excitation period could be either 8 
inches, the diameter of the cylinder, or 9-1/2 inches, the maximum tip to tip beam. This 
accounts for the range of values of excitation period shown in F'ig. 10. 
In general, as would be expected, the closer the correspondence between the natural 
roll period and the period of excitation, the larger the roll amplitude that resulted. It might 
be noted that it is very likely that the actual natural roll periods of the model during some 
of these tests were longer than the computed periods because of leakage. A moderate 
increase in the natural roll periods of some of the test spots would have improved the corre- 
lation between maximum roll amplitude and resonance. 
While the proximity to resonance explains several of the large observed roll amplitudes 
in Fig. 10, in most instances the test conditions with low metacentric heights (large natural 
periods) showed larger roll amplitudes than conditions with large metacentric heights (small 
natural period). Although not directly apparent from Fig. 10, the preceding statement applies 
at constant tuning factor (ratio of natural period to excitation period). For example, the 
comparison of results of test 14 to tests 10 and 7 or test 11 to test 4 shows this tendency. 
The only exception to this pattern are tests 13 and 17. This effect of metacentric height is 
consistent with vibration theory (e.g., Ref. 8). 
Only data for the narrow bilge keel tests of July 27-29 are shown in Fig. 10 since none 
of the wide keel tests showed strong oscillations and, in fact, most of those tests showed 
no oscillations at all. Therefore, it may be concluded that a substantial reduction in roll 
amplitude can be achieved with wider bilge keels. However, this is achieved at the expense 
of a considerable increase in vertical drag (see Fig. 11), particularly in the range of full- 
scale Reynolds number where the bare cylinder drag is a much smaller fraction of the total 
than it is in the model range. 
In addition to quantitative data on roll amplitude and vertical velocity, the free ascent 
tests revealed strong cross-coupling between vertical forces and horizontal motion. As a 
result, the model usually achieved some ahead velocity while solely under the influence of 
a vertical force. This cross-coupling is probably enhanced by the strong fore and aft asym- 
metry introduced by the presence of large stern fins. Usually, only a slight pitch or yaw 
developed during the tests. However, during test 16 a strong pitch developed. Nevertheless, 
in no case was there evidence that the coupled motions prevented the predicted occurrence 
of roll oscillations. 
