Deep-Diving Submarine Hydrodynamics 309 
capsule is pressure equalized to the open sea at all times so that it may be constructed of 
relatively light structure. Figures 1 and 2 show the general configuration of the submarine. 
The configuration, thus determined, has somewhat different proportions than the usual 
military submarine. The length/diameter, L/D, ratio is lower and the prismatic coefficient, 
Cy, (ratio of volume of submarine to volume of circumscribing cylinder) is higher than the 
corresponding proportions of military submarines. These properties of the Aluminaut are 
conducive to minimizing wetted surface and hence frictional drag at the expense of an 
increase in separation and form drag. The differences in wetted surface between the 
Aluminaut and military submarines and the wetted surfaces of elementary body of revolution 
shapes similar to submarines are shown in Fig. 3. ‘The ordinate of this figure is the wetted 
surface of solids of unit volume. (For example, a cubic prism of unit volume has a wetted 
surface of 6.) To compute the wetted surface of geometrically similar volumes, it is only 
necessary to multiply the value of the ordinates in Fig. 3 by the volume raised to the 2/3 
power. It is seen that not only does the Aluminaut have substantially less wetted surface 
than military submarines because of her low L/D and high C,, but with those proportions 
her hemispherical nose and essentially conical stern offer almost as low wetted surface per 
unit volume as the less hydrodynamically satisfactory combination of conical nose and 
stern. The comparison is as follows at the Aluminaut L/D and C,: 
Con fi guration Wetted Surface for Unit Volume 
Hemi-nose; conical tail 6.90 
Conical nose; conical tail 6.89 
The additional useful information shown in Fig. 3, computed on the basis of information 
given in Appendix A and taken from Fig. 7 of Ref. 2, is in the nature of a postscript to the 
main purpose of this paper. Primarily, the figure shows the large penalty in wetted surface 
associated with high length/diameter ratios, which is well known, and the variation of 
wetted surface with prismatic coefficient and end shape, which is not so well known. Within 
the range of L/D’s suitable for streamlined bodies (L/D>3) and at low values of Cp, the 
bodies with conically shaped nose as well as tail, have the least wetted surface, the bodies 
with hemispherical noses and conical tails have the next greatest, while bodies with sub- 
marinelike noses and tails have the most wetted surface. This latter fact is consistent with 
the frequent observation that achieving reasonable form drag usually involves increased 
wetted surface and frictional drag. At high prismatic coefficients the effect of end shape 
on wetted surface is not nearly as decisive as at low values of C,. It might also be 
observed that to achieve the complete continuity at the intersections of the parallel middle 
body and the end shapes that is needed to minimize form drag, and that is so obviously 
missing with pure conical or even hemispherical ends, much higher prismatic coefficients 
are associated with a fixed percentage of parallel middle body L,,’ for the submarinelike 
bodies than for the simpler shapes. All in all it is evident from Fig. 3 that the L/D ratio is 
the most important parameter influencing wetted surface and that prismatic coefficients in 
the practical range from 0.50 to 0.90 are also conducive to minimizing wetted surface for 
any fixed L/D ratio. For a more thorough discussion of this particular question, the reader 
is referred to Section 3 of Ref. 2. 
Figures 1 and 2 indicate that the Aluminaut is encumbered with many appendages. 
Most of these are needed to house equipment or ballasting functions (described subsequently) 
that are advantageously mounted external to the main pressure hull. As shown in Fig. 2, and 
also subsequently in Fig. 6, some of these appendages are not suitably faired, but this prob- 
lem is fully appreciated by all concerned and it has been decided that the building plans 
will incorporate suitable fairings. Even faired, it is estimated that the appendages will more 
than double the bare hull-drag of the submarine in horizontal motion. Drag estimates will 
be shown in Fig. 13. 
