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Statement Of Metacentric Heights And Stability, Based On An Inclining Experiment hade On The Ship On March 27, 1900.
A. The ship when fully equipped, with reserve feed-tanks empty, with 300 tons of coal in lower bunkers and 300 tons of coal in upper bunkers, at a mean draught of 20 ft. G in. has a metacentric height of
B. The ship when fully equipped, with fresh
water and reserve feed-tanks and all
When lightened to a mean draught of 18 ft. 3
The angle at which the ship reaches her maximum stability in the above condition A, and beyond which the righting force diminishes, is about
The angle at which the ship reaches her maximum stability in the above condition B, and beyond which the righting force diminishes, is about
The angle at which her stability entirely vanishes in the above condition A is about
The angle at which her stability entirely vanishes in the above condition B is about
Note.—So far us stability is concerned the coal may be worked in any manner desired by the Commanding Officer.
THE ROLLING OF SHIPS.
Rolling in Still Water.—Rolling in still water is of no immediate practical importance, because under ordinary circumstances a ship will not roll in still water. It is, however, necessary to study the subject, because it is only when the conditions operating in this case are understood that we are able to extend the inquiry to the more difficult case of rolling among waves.
If a ship, floating upright in stable equilibrium in still water, is inclined to a certain angle 0 from the upright, the couple tending to take her back to the upright is Wx GZ. If the ship is released she will acquire angular velocity, passing through the upright to an angle on the other side rather less than 0. At this new angle, 0', say, she will have a couple tending to take her back to the upright, and so the ship, once being inclined and released, will continue to oscillate through smaller and smaller arcs of oscillation until she finally comes to a position of rest. When the ship is inclined to the angle 0 as above, it is necessary to do work on the ship to effect the inclination, and this work is stored up in the ship as potential energy, or energy due to position. When the ship is released, this energy becomes converted into other forms of energy, and, if no resistances were operating tending to stop the motion, the ship, when passing through the upright, would have kinetic energy, or energy due to motion, exactly equal to the original potential energy.
This conversion of energy of one form into energy of other forms is well seen in the case of a stone on the top of a house. In some way work has had to be done to get the stone there, and the stone, in virtue of its position, has stored up in it a certain amount of potential energy. If the stone is released, it will reach the ground with a certain velocity, and (neglecting the friction of the air) the kinetic energy then possessed is equal to the original potential energy. When stopped by the ground both potential energy and kinetic energy disappear, but the energy is not lost, but is dissipated into the form of heat energy.
In the case of a ship rolling unresistedly the energy is alternately potential and kinetic at the extremity and middle of each roll, and the rolling would go on continuously; but when resistances operate, the energy gets drained away from the ship and becomes finally dissipated by imparting heat and motion to the air and water surrounding the ship.
Unresisted Rolling in Still Water.—It can be shown that for unresisted rolling in still water the period of a single oscillation (from port to starboard, or vice versa) is very nearly given by
T = 0-55x/jL seconds
where GM is the metacentric height and k is obtained from the following definition:—
The moment of inertia of a solid body about any axis is found by adding together the product of each weight making up the body and the square of its distance from the axis. (This is analogous to the moment of inertia of a plane area about an axis, dealt with in Chapter XVII.) If for a ship this axis is the axis of oscillation, W the weight and I the moment of inertia about the axis, then k is such a quantity that I = W X k2, and k is termed the radius of gyration.
The calculation for k is a most laborious one, but it has been done in a few cases, and having also the metacentric height, an estimate could then be made of the time of oscillation from the above formula. Practical agreement was found to exist between the actual and the estimated times of oscillation, even although the rolling could not have been unresisted.
The formula shows that to make the period long, i.e. to increase the time of oscillation, it is necessary to
(1) increase the radius of gyration, and, or (2) decrease the metacentric height. (The longer the period of a ship the more likely is she to be steady in a seaway.) Of these two, the first is of the lesser importance, because the distribution of the weights is governed by other features of the design than the desirability of obtaining a long period. The formula, however, shows clearly that winging weights, i.e. placing them at the sides, operates in the direction of increasing the period, although any practicable shift of weights on board a war-ship can only have a small effect on the period. We should expect, therefore, to find that an armoured ship would roll more slowly than an unarmoured ship of about the same displacement and metacentric height, and this is confirmed by experience of ships in the Royal Navy.
A very considerable effect in lengthening the period is obtained by reducing the metacentric height Thus in the Royal Sovereign, in which ship the period is 8 seconds and the GM about 3£ ft, suppose the GM is reduced to 3 ft., without altering the radius of gyration. Then we should get a period of 8-64 seconds, or an increase of 8 per cent.
An interesting application of the above principles is found in the current practice of many merchant vessels. In many trades, voyages have to be undertaken with little or no cargo, because of the absence of return freights. It is necessary, for seaworthiness and proper immersion of the propellers, to sink the vessels by means of water-ballast. This has usually been placed in the doublebottom compartments. This, however, frequently pulls down the C.G. of the ship so far as to give the ship a large GM. This causes a very quick period, and in some cases this has not merely rendered the ship uncomfortable, but actually unsafe. In many ships, therefore, it is the practice to provide tanks in the 'tween decks and hold at the sides, and even on the upper deck. These tanks below are frequently large enough to hold ordinary cargo when necessary, but for ''light" voyages they can be filled with water. The weight thus added, while giving sufficient immersion, does not produce excessive GM, and being at the sides tends to lengthen the period by increasing the radius of gyration.
The assumption used in obtaining the above formula for the period from side to side, viz. T = 0-55\/ SLJ is, that the righting
lever varies directly as the angle or GZ = GM x 0, i.e. it assumes that the curve of stability is a straight line up to the angle considered. Under this condition large and small inclinations will be performed in the same time. A ship rolling in this manner is said to be isochronous.
Although the various assumptions made in obtaining the above formula are not strictly true, yet it is found by actual experiment that, within angles of 10° to 15° of the vertical, ships are very nearly isochronous in their rolling. This is the case although the ship experiences resistances which eventually bring her to rest.
The following are the approximate periods of some typical ships, i.e. the time from port to starboard, or vice versa.
e A vessel of large GM., via. 8 ft., causing a Inflexible 5 V Sees. < small period. This was the cause of the ( introduction of water chambers (see later).
Royal Sovereign ) ( ^P8 of m<*lerate GM- about 3} ft, and
M • . ■ \ 8 sees. < great moment of inertia, due to beam and
Majestic j J armour at skies.
Powerful 7 sees. \
Arrogant 6 sees. } Protected cruisers with no side armour.
Pelorus 5£ sees. )
Gunboats and I gecg , Small period due to (a) small moment of
Destroyers J * i inertia; (6) relatively very large GM.
Resisted Rolling in Still Water.—Under the actual conditions under which a ship will roll in still water, resistances to the rolling are set up which drain the ship of energy and which sooner or later will bring her to rest. These resistances may be classified as follows :—
1. Friction of water on the ship's surface.
2. Effect of sharpness of form of ship's section.
3. Effect of bilge keels or keel projections (if any), including the flat portions of the ship.
4. Creation of waves on the surface. 5 Air resistance.
6. Use of water chambers.
1. Friction.—This cannot be of great amount in ordinary ships, because the surface is kept smoothly painted to reduce the resistance when steaming to the smallest possible amount.
2. Form of Section.—In a ship of circular section the relative velocity of the water and the surface of the ship is the same at all points of the section. In a ship of sharp form at the bilge, however, the water at the corner gets a motion opposite to the ship, and having to slip past the bilge, the effect both as regards friction and on bilge keels is greater in a sharp bilge than in a rounder form of section.
3. Bilge Keels.—The reason of the great extinctive effect of bilge keels in reducing rolling has been imperfectly understood until recently. The explanation is of considerable difficulty, and the following remarks do not pretend to completely deal with the subject:—
(a) A bilge keel is like a flat surface passing through water broadside on. The laws governing the resistance of such flat surfaces have been investigated, but in applying them to the case