534 Edward V. Lewis and John P. Breslin 
exercised to remain in the subcritical speed range in following seas. The basic idea is 
simply to attain high ship speed and a long, natural pitching period. The problem of high 
speed involves the question of reducing wavemaking resistance, which has already been 
discussed. 
To consider all the possible means of increasing the natural pitching period GG ) it is 
well to examine the equation given in Ref. 5: 
(1) 
in which V is displacement volume, g is acceleration of gravity, B is breadth, and L is 
length. The coefficient C, is the inertia coefficient so that the longitudinal mass moment - 
of inertia J, =-Ve(C,L)?, or C, = 1I/L J, /Ve; (C 7k, is an analogous coefficient of virtual 
inertia by which VpL?2 must be multiplied to give the longitudinal mass moment of inertia of 
the entrained water. C,, is the coefficient of longitudinal waterplane inertia defined by the 
relationship 
3 
EY BOB 
From Eq. (1) it can be seen that the following trends increase the natural pitching 
period: 
1. Increase of displacement 
2. Reduction of length or beam 
3. Increase in virtual inertia (C,7k,) 
4. Reduction in waterplane inertia (C,, ) 
5. Increase in mass moment of inertia (C,). 
Because a ship in supercritical operation tends to plunge through the waves rather than 
to ride over them, it is difficult to attempt to keep water off the foredeck. Accordingly, low 
freeboard and a heavily built deck is one way to cope with shipping of water, which at the 
same time permits a very narrow waterline. The body plan in Fig. 5 illustrates a possible 
design for a supercritical ship of this type, (Z) of Fig. 1, a ship like a surfaced submarine, 
made longer and more slender to attain high surface speed. The normal waterline would be 
used for good weather operation; in bad weather, large peak ballast tanks would be filled to 
lengthen the pitching period by increasing the displacement, by increasing the radius of 
gyration, and by reducing the waterplane area (items 1, 4, and 5 above). Characteristics are 
compared with a typical destroyer in Table 1. 
This semisubmerged model had T p/VE = -0.38 in the deep-draft condition. Results of 
tests in regular- and irregular-head seas [3] confirmed theoretical expectations that a super- 
critical condition of moderate motions could be attained at speeds of 35 to 40 knots in mod- 
erately rough irregular-head seas (Fig. 6). Heaving motions were more pronounced than 
