In ancient times there were three principal things beyond human comprehension: the way of a bird in the air, the way of a ship on the sea, and the way of a man with a maid. Scientific research during the" past few years has done much to clear up the first two subjects. This discussion will deal with the ship on the sea; in particular the rolling of the ship.
Everyone knows that ships at sea sometimes roll. Some ships roll more than others. It is not uncommon during discussions to hear a ship referred to as a “roller.” Generally the fact that a particular ship is prone to roll heavily on the slightest provocation is accepted by the personnel simply as an unfortunate attribute of that ship without any thought or idea of why she rolls; just as it is accepted that some people have blue eyes. There are, nevertheless, definite reasons why some ships roll more than others. Experiments and research are bringing these reasons out more and more clearly and indisputably.
The roll of a ship is very much like the swing of a pendulum. It has two properties, amplitude and period. When we know these two characteristics for a single roll of a ship we know all about that roll. Amplitude is the angle of heel to which the ship goes over. Period is the time of a single roll, usually taken for a roll from one side to the other (for example, from maximum list to port to maximum list to starboard). Great angles of roll are objectionable not only because of the inconvenience to personnel but also because of the added difficulty in handling and fighting the ship. When a ship is rolling 20°, 25°, or 35° on a side, it is quite a problem to maintain water levels in the boilers, let alone serve the guns. A short period, that is, a quick roll, is also undesirable. When a ship rolls quickly she has a “snap” that not only causes great stresses in structure and rigging but is also very disconcerting to anyone trying to take observations or hold a gun or director sight on an object.
Except in cases where rolling of a ship is produced by artificial means a ship at sea is caused to roll only by waves. It has been pretty definitely established that the rolling of a ship depends on: The ratio of the period of the ship to the apparent period of the waves; the slope of the waves; the damping of roll characteristics of the ship. The generally accepted theory of rolling bristles with complicated differential equations and other mathematical nightmares. However, an understanding of the nature of these three points can be had without going into the mathematics.
Suppose a ship to be steaming on a calm sea, when a single wave approaches from the beam, the crest line of the wave being parallel to the course of the ship. As the face of the wave passes the ship the latter is no longer on a horizontal surface of water such as the calm sea but is on an inclined plane of water, and rolls downhill, away from the crest. The bottom of the roll is reached as the crest passes the ship. Now the ship is on the back slope of the wave which is inclined oppositely to the face. Again the ship rolls downhill, in the direction of upright from the heel imparted by the face of the wave. In this case, however, the roll due to the slope of the back of the wave is aided by the stability of the ship which is working to bring the ship upright. The righting force of stability and the inclination of the back of the wave give the ship such an angular velocity that she will carry on past the upright to an increased inclination on the other side and, after the wave has gone by, will continue to roll in her own natural period gradually coming to rest in an upright position.
Now, if instead of a solitary wave, there is a series of waves of such distance between crests and such speed of travel that the time required for successive crests to pass the ship is twice the natural period of roll of the ship (from port to starboard or vice versa) then the stability force at maximum heel will always be working with the wave slope and every passing wave will increase the angle of roll of the ship. If there were nothing to oppose this roll the ship would eventually capsize. This case is the so-called synchronous rolling. The sketch shows graphically the condition here described.
It can be proved that if the roll of the ship is unresisted each passing crest and trough of a synchronous wave series will increase the amplitude of roll by the amount pi/2y, where y is the slope of the wave. This is indicated in the sketch.
An inclination of a ship is resisted by its stability forces; but in the case of rolling in synchronous waves it has been shown that these forces work to increase the angle of roll. The gradual building up of amplitude must be opposed by forces other than stability. These forces are called damping forces. Actually there is no such thing as unresisted rolling; damping is always present. The friction of the skin of the ship moving through the water opposes rolling. Dynamic damping is obtained by installing bilge keels, the resistance of the latter to being swished through the water brings tremendous forces to act against the roll. Gyro stabilizers and anti-rolling tanks are sometimes used to oppose rolling. All of these devices have one common goal, the creation of damping forces to resist the roll.
Suppose our assumed ship has such damping characteristics that when she is heeled to an angle 9 on one side and released she will roll to a lesser angle 9, on the other side. The damping acts nearly according to the law.
(0-01) = b02
That is, the angle by which each roll is diminished is equal to a constant b times the square of the angle of heel at the start of the roll; b is the “damping factor” of the ship.
It has been explained how each trough and crest of the synchronous wave train increases the angle of heel of our ship by the amount pi/2y. The damping decreases each roll by the amount b02. It can easily be seen that the ship will build up a roll until an angle of heel 9 is reached such that b02=pi/2y. When this point is reached the increment added by the wave is equal to that subtracted by the damping and the ship will roll with constant amplitude 9 as long as conditions assumed remain unchanged.
O, the angle of wave slope, is determined by the height and length of the waves. Available data on sea waves indicates that the speed of travel of a well-established wave train is about the same as the speed of the causative wind. The length and period are related by the formula, T = /(2piL/g). The height is nearly equal to the square root of the length.
Early in this discussion it was stated that the rolling of a ship at sea depended on the ratio of the period of the ship to the apparent period of the waves, the wave slope, and the damping of roll characteristics of the ship. The parts played by the wave slope and the damping have been discussed.
Suppose that the wave train acting on our ship has a period shorter than that of the ship. Then when the trough following the first crest reaches the ship she will not have reached her maximum angle of heel but will still be rolling away from the first crest. The face of the second wave will then find the ship rolling toward the second crest and a part of the slope will be used to bring the ship to rest reducing the maximum angle of heel. If the period of the waves is longer than that of the ship the maximum heel will be reached before the wave slope has passed and the ship will start back in opposition to the wave slope again reducing the maximum heel. The farther removed the period of the waves is from the period of the ship the greater the opposition of the waves to the natural roll. In non-synchronous waves the ship is finally forced out of her natural period of roll and made to roll in the period of the waves. The angle of roll in these cases is small, being seldom more than the wave slope. When the wave period and ship period are nearly synchronous, the angles of heel may reach considerable magnitude. For ratios of ship period to apparent wave period of 0.9 to 1.1, heaviest rolling may be expected (the amplitudes depending on wave slope and damping).
Wherever periods have been mentioned care has been taken to designate the apparent period of the waves. The apparent period of the waves is the time required for successive crests to pass the ship. If the ship is steaming parallel to the crest line of the waves the apparent period is the actual period of the waves. If the ship is steaming at an angle to the crest line the apparent period of the waves will be increased if steaming with the waves, and decreased if steaming into the waves.
It is assumed throughout this discussion that the waves are of considerable size compared to the ship. For a ship of 60-foot beam or more, waves less than 400 feet in length would hardly affect her even when lying in the trough. Long ships steaming at an angle to the crest line might span two waves of short length in which even the effect of the waves would be small. Waves to synchronize with a ship of 14-second period in the trough would have to be 1,000 feet long. Such waves are rarely met. The longer the period of a ship the less chance there is of her meeting synchronous waves whether steaming parallel to the crests or at an angle.
The question naturally arises “Why not give all our ships long periods and avoid rolling?”
The period of a ship is determined by the moment of inertia about a fore-and-aft axis and by the metacentric height. For a ship required to have definite characteristics the moment of inertia is practically fixed. The designer then can control the period by varying the metacentric height (GM). Unfortunately, the greater the GM the shorter the period. Naval vessels are designed to be able to sustain heavy damage and still keep on fighting. As a ship is damaged and compartments flooded she loses stability rapidly. For this reason, a naval vessel must be given excess stability in the undamaged condition; that is, a large value of GM. This decreases her period which makes her susceptible to rolling. We have, then, still another compromise on our hands.
Recent research leads to the hope that damping may be made more efficient than it has proved heretofore and as a result the high seas made more comfortable for short period ships.