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many harbors is less dense than salt sea water. Consequently, the ship rises somewhat and draws less water as soon as it floats in sea water. According to the size of the ship and the density of the water where it loads, some 2, 4, or 6 inches may be allowed for this contingency. This is known as "allowance for density."

PAYABLE TONS

There are only two items of cargo on which the rate is charged on the basis of weight-800 tons of oil cake, stowing 35 feet per ton, and 1,000 tons steel billets, which stow at 12 feet per ton. All the other cargo stows from 50 to 150 feet per ton weight, so the space occupied, and not the weight, is the main consideration in figuring the freight charges. For "payable tons" purposes, therefore, this is measurement cargo, and payable tons will figure thus:

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The "payable tons" in this instance represent a gain of nearly 38 percent over the ship's deadweight capacity, and about 122 percent over the cubic capacity. The example serves to illustrate how the loading of a vessel full and down by a careful selection of cargo (when such selection is possible) and its proper stowage, results in building up the voyage revenue.

CHAPTER VI

STOWING TO PREVENT DAMAGE OR DANGER TO THE SHIP OR CREW

[Adapted, in large measure, from Stowage of Ship Cargoes, Miscelaneous Series No. 92, chapter III, Bureau of Foreign and Domestic Commerce]

A ship may be damaged or destroyed, its efficiency impaired, or the lives of its crew endangered by improper stowage. Vessels have been lost from this cause, and it is incumbent upon everyone connected with the operation of oceangoing vessels to acquaint himself with the most common causes of such losses and the means by which they may be averted. The principal types of improper stowage which endanger the ship and crew are those which affect the stability of the ship and those which may contribute to the breaking out of fire.

The discussion of this aspect of stowage will be divided under the following heads: Improper vertical distribution of weights; Improper longitudinal distribution of weights; Improper transverse distribution of weights; Shifting of cargo; Damage caused by character of cargo; and Damage caused by stowing cargo in heated parts of the vessel or where there is danger of fire.

IMPROPER VERTICAL DISTRIBUTION OF WEIGHT

Improper vertical distribution of the cargo may give rise to danger largely because of its effect on the vessel's rolling.

Rolling, or the movement of the vessel from side to side, may result in injury to the ship, damage to the cargo, and loss of speed. If excessive, it may lead to the foundering of the ship. Because of its importance and because it can be controlled in part by the disposition of cargo, the ship operator and stevedore should understand its causes and the measures to be taken for its reduction.

There are two distinct problems here. One is that of stability; and the other the amount and speed of rolling; or, in other words, one problem is the danger of capsizing the ship and the other the damage done by excessive rolling. The fact that a ship is stable does not necessarily mean that it rolls relatively little. In fact, quite the contrary may be true.

STABILITY

With present-day ships it is less difficult than formerly to practice stowing methods that improve the stability of the ship. But even now many ships are easily upset by poor stowing, combined with heavy weather, and all may be endangered by gross carelessness in stowing.

The stability of a ship is its power to right itself when rolled to one side. This power depends upon the relation of the center of

gravity of the vessel and the center of buoyancy of the water displaced by the vessel.

Suppose a ship to be lying under normal conditions in still water (see fig. 48). The water line is represented by WL, the center of gravity by G, the center of buoyancy by B. Now, suppose the vessel to be rolled to a new position, so that the water line is W'L'. Unless the load has shifted, the position of the center of gravity remains the same, but the position of the center of buoyancy has shifted to B'. Draw a line through B' perpendicular to W'L' and a line through B perpendicular to WL. Their intersection M is called the metacenter. Draw a line through G perpendicular to B'M and intersecting B'M at Z.

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The weight of the ship acts downward through G, and the pressure of buoyancy (equal in force to the weight of the ship) acts upward through B'. The force tending to return the ship to its original position is therefore a movement whose arm is GZ and whose weight is the weight of the ship. The weight of the ship remains constant: therefore the righting force depends upon the length of GZ, and GZ is called the righting lever.

STIFF AND CRANK VESSELS

From the figure it will be seen that if G and M coincide there is no righting lever, and the ship will stay in the position to which it has been moved. If M is above G the movement tends to return the ship to its original position; if M is below G the movement tends to move the ship still farther from its original position. In other words: (1) If the metacenter (M) is above the center of gravity (G) the ship is in stable equilibrium; (2) if the metacenter (M) coincides with

the center of gravity (G) the ship is in neutral equilibrium; and (3) if the metacenter (M) is below the center of gravity (G) the ship is in unstable equilibrium. In shipping language the ship is "stiff" if M is far above G, and "crank" if M is above but close to G.

Hughes states that the "minimum value of the distance between the center of gravity and metacenter (GM) in steamers of medium size is about 1 foot when loaded with a homogeneous cargo that brings them to the load water line. For small cargo vessels the distance between the center of gravity and the metacenter should be not less than 9 inches, provided a righting arm of like amount is obtained at 30° to 40°. For sailing vessels a higher value of GM is required, the minimum being 3 feet to 3 feet 6 inches with a homogeneous cargo.'

The proper vertical point for the center of gravity varies with the vessel and the cargo. If the center of gravity is too high, the vessel is likely to capsize. The beam and the freeboard help to determine the stability of the vessel, but the position of the center of gravity is the most important factor. If the center of gravity is low, there will be a strong force tending to return the ship to a vertical position after it has rolled to one side. If it is high, the force will be weaker;

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and if it is too high there will be no return movement and the vessel will roll over.

If the center of gravity is very low the righting force will be so great that the vessel will be brought up with a jerk, carried beyond the vertical position, and will then oscillate or roll until equilibrium is established. There is absolutely no danger of capsizing, but there is danger that the excessive rolling will strain the vessel and cause chafing and shifting of cargo. A ship in this condition is said to be "stiff," as contrasted to "crank" (see above) which is the term used to express an unstable condition.

The values of GZ (the righting lever) for different inclinations of a ship can be obtained by calculations. These values can be plotted, and the result is the "stability curve" of the ship. For the same ship a number of curves should be plotted to show the stability of the ship under different conditions of load. Figure 49 shows such a group of curves. From these curves the master of a ship can determine the value of the force tending to right the ship at a given angle of inclination under a given load.

The master of the ship should have, and should be able to interpret, the curves of stability for his ship, and he must go further

1 Hughes, Charles H. Handbook of Ship Calculations, Construction, and Operation. D. Appleton & Co., New York 1918.

than this. Obviously curves cannot be constructed to cover every possible condition of loading, and the master should be able to construct his own curves for variation in load. It is absolutely necessary that he determine the stability for loads that may cause danger. But what sort of load is dangerous?

From figure 48 it will be seen that the length of the righting lever depends upon (1) the height of the metacenter, M; (2) the position of the center of buoyancy, B; and (3) the position of the center of gravity, G.

The length of the righting lever will increase with increase in height of M, with change in the position of the center of buoyancy, and with decrease in height of center of gravity. Therefore the master must know what causes bring change in the positions of M, B, and G.

The height of the metacenter (M) depends largely upon the beam of the vessel and is fixed for small inclinations. Since alteration in stowing can make no change in the beam of the vessel, the ship's officers need not consider this factor.

The change in the position of the center of buoyancy depends primarily upon the freeboard of the vessel. If the freeboard is large, the position of the center of buoyancy will move farther at a given inclination than if the freeboard is small. Therefore a large freeboard means increase in stability, other things being equal. This has been recognized by maritime interests, and the minimum amount of freeboard has been prescribed by Lloyds, the American Bureau of Shipping, the Bureau Veritas, and by naval architects and shipbuilders.

In almost all cases, as the freeboard increases the center of gravity will rise; and raising the center of gravity may mean decrease in stability. The master cannot make his freeboard so small as to incur danger, for he is prevented from so doing by maritime law; and ordinarily he will not make his freeboard too large, because he wants his ship to carry the maximum load. If the amount of freeboard does become too large he will need to inquire into the position of the center of gravity.

Changing the position of the center of gravity is the most important way of changing the ship's stability and is at the same time. the method that is most under the control of the master of the ship. In a cargo vessel the position of the center of gravity depends very largely on the disposition of the cargo, ballast, and stores. If most of the weight is low in the hold, the center of gravity will be low, the righting lever long, and stability assured. If the weight of the cargo is placed high, or if there is very little weight to the cargo, the center of gravity will be raised, the righting lever shortened, and the ship's stability endangered.

In every case, therefore, in which the character or disposition of the cargo is such as to indicate a rise in the center of gravity, the master should draw stability curves. The method of doing this is described in various handbooks, but essentially it consists of multiplying the distance the center of gravity has been raised by the sines of different angles of inclination, deducting the results from the original righting levers for those angles of inclination, and using the values thus obtained to lay off a new curve. If the new curve indicates stability the master may proceed in safety; but if the

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