532 Edward V. Lewis and John P. Breslin 
another [6]. They also have confirmed the observations of seamen that shorter waves are 
formed first in a storm. As the wind continues to blow, longer components are formed with- 
out seriously affecting the smaller components. For a particular wind velocity, the sea 
reaches a limit when it attains its fully developed state. If the wind increases in strength, 
not only are the component waves believed to be higher, but — when the fully developed 
state is reached — longer components also will be present. 
If a ship is able to attain a speed sufficiently high that its period of encounter with the 
longest important wave component is shorter than the natural pitching period, the ship will 
be in the supercritical condition for that particular storm. Most ships can attain this condi- 
tion only in moderately heavy seas — that is, in light winds or in stronger winds of short 
duration. In general, whether or not a ship can attain the supercritical condition depends 
both on the sea state, indicated by wind velocity and duration, and on the ship’s natural 
pitching period. Speeds for supercritical operation are shown for the case of head seas in 
Fig. 4, which is taken from Ref. 5. At other headings, the ship must reach even higher 
speeds to attain the supercritical condition. 
Because short waves are present in both severe and moderate storm seas, it is impos- 
sible to avoid synchronism with all component waves by reducing speed. However, model 
tests have shown that waves appreciably shorter than the ship do not cause serious motions 
even at synchronism. Therefore, speeds that are low enough to avoid synchronism with 
waves of ship length and longer cause moderate motions. This condition may be termed the 
subcritical range. For head seas, it depends mainly on the ship length and the natural pitch- 
ing period, that is, on the ratio T /VL, as shown in Fig. 3. At times, all ships must reduce 
speed in storm seas to attain the subcritical condition of moderate pitching. 
In following seas, most ships steaming at ordinary speeds are always in the subcritical 
range. This explains the advantage of heaving to with wind and sea astern, provided that 
the ship can be kept under control. However, Mandel [7] has pointed out that unusual ship 
forms intended for supercritical operation in head seas may encounter critical conditions in 
following seas. 
SUPERCRITICAL OPERATION IN ROUGH SEAS 
It has been shown in Ref. 5 that for most ships the most promising method of reducing 
pitching and heaving motions is to use hull proportions that raise the critical-speed limit 
and permit higher subcritical speeds. This means increasing the length in relation to dis- 
placement, which results in a reduced period-length ratio, T,/VL. A ship can then go at 
higher speed before synchronous response to waves of near ship length is experienced 
(Fig. 3). 
Thus, in Ref. 8 a model 25 percent longer than a conventional DD-692 destroyer, but 
with the same displacement, had lea ta = 0.20 instead of 0.25. It was concluded that in a 
storm in which the conventional destroyer could attain a speed of 20 knots (V//L = 1.0), 
the longer vessel could attain a speed of 30 knots or V/\/L = 1.4 (Fig. 3). The longer 
destroyer was an abnormally slender ship, with A/(L/100)3 = 30. Tremendous problems of 
stability, structure, and hull arrangements would be encountered in the design of such a 
ship. It hardly seems feasible, therefore, to think of large increases of speed to 50 or 60 
knots by going further in the direction of longer and thinner ships. 
The most promising direction then to obtain really high speeds in head seas, where mo- 
tions are most severe, is to aim at supercritical operation. At the same time, care must be 
