530 Edward V. Lewis and John P. Breslin 
band of wave periods (or frequencies) than to any others. This period is the natural rolling 
period of the ship. Consequently, the most serious rolling occurs in the natural period of 
the ship and, therefore, may be classed as synchronous rolling. In any oscillating system, 
simple damping is always effective in reducing synchronous oscillation. Therefore, by in- 
creasing the damping of roll, the bilge keel markedly reduces serious synchronous rolling. 
Another damping device is the passive antirolling tank system, in which there has been 
a notable resurgence of interest recently. Such tanks installed in naval auxiliaries have 
proven to be remarkably effective. Important features are their low installation cost and 
equal effectiveness hove to and at forward speed. However, reduction rather than elimina- 
tion of rolling is the best that can be expected. 
For moderate and high-speed vessels, a much more effective method of reducing rolling 
appears to be controllable fins. These devices are so effective that the rolling problem ap- 
pears to have been solved in principle, except for low-speed vessels for which an activated 
tank or gyroscope system is applicable. This does not mean that further research is not 
needed. There are problems of the interaction or coupling of other motions, particularly 
yaw, of obtaining increased effectiveness with reduced weight and cost, of avoiding struc- 
tural failures of fin shafts, etc. Furthermore, the system for the control of roll must be co- 
ordinated with the system for the control of yaw, that is, the steering gear and gyro-pilot. 
Heaving and pitching motions are the most difficult to overcome and present the most 
serious problems because they involve large vertical accelerations and cause shipping of 
water, slamming, and propeller racing. Furthermore, when other motions are controlled or 
reduced, they become even more noticeable. Consequently, attention will be focussed on 
these symmetrical modes of motion, assuming that methods are available for solving the 
other motion problems. 
Model research in regular-head seas has brought three important facts into prominence 
[5]: (a) the amplitudes of motion are greatest in the vicinity of synchronism between the 
period of encounter and a ship’s natural period of oscillation, (b) phase relationships lead- 
ing to wet decks and slamming also are characteristic of synchronism, and (c) waves appre- 
ciably shorter than the length of a ship do not cause serious motions even at synchronism. 
On the basis of these general facts, there are two possible methods by which significant 
reduction of pitching and heaving amplitudes can be sought: avoiding synchronism with 
waves of ship length or longer, and reducing the magnification effect, which causes in- 
creased amplitudes near synchronism. 
Although damping devices such as bow fins can reduce the magnification of motions 
somewhat, the most effective method of reducing motions is by avoiding synchronism. Ina 
regular swell, this undesirable condition can be avoided by changing either course or speed. 
If the speed is changed, synchronism can be avoided by an increase or a decrease. If the 
speed for pitch synchronism is the critical speed, slowing brings the ship into the subcriti- 
cal range; increasing speed brings the ship into the supercritical range. Figure 3 (from 
Ref. 5) shows the relationship between pitching period and speed for synchronism in head 
seas. For other headings, a simple cosine correction must be introduced. The curves that 
define the conditions for synchronous pitching show that (a) the longer the wavelength, the 
higher the critical period, and (b) in any particular wavelength, the lower the ratio of T,/VL, 
the higher the critical speed. 
When a ship encounters irregular storm seas, the situation does not remain so simple. 
Oceanographers have shown that storm seas can be considered as composed of a great many 
regular-wave trains of varying length and direction of travel, all superimposed on one 
