Naval

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CHAPTER 2 STABILITY

2-1 INTRODUCTION This chapter discusses the stability of intact ships and how basic stability calculations are made. Definitions of the state of equilibrium and the quality of stability as they apply to ships are given in the following paragraphs. 2-1.1 Equilibrium. A ship floating at rest, with or without list and trim, is in static equilibrium; thatis, the forces of gravity and buoyancy are balanced. They are equal and acting in opposite directions and are in a vertical line with each other. 2-1.2 Stability. Stability is the measure of a ship’s ability to return to its original position when it is disturbed by a force and the force is removed. A ship may have any one of three different kinds of stability, but only one at a time. 2-1.2.1Positive Stability. If the ship tends to return to its original position after being disturbed by an external force, it is stable or has positive stability. 2-1.2.2 Negative Stability. If the ship tends to continue in the direction of the disturbing force after the force is removed, it is unstable or has negative stability. 2-1.2.3 Neutral Stability. A third state, neutral stability, exists when a shipsettles in the orientation it is placed in by the disturbing force. Neutral stability seldom occurs to floating ships, but is of concern in raising sunken ships because a ship rising through the surface passes through a neutral condition. While the ship is neutrally stable, even a very small disturbing force may cause it to capsize. 2-2 TRANSVERSE STABILITY Transverse stability is the measure of aship’s ability to return to an upright position after being disturbed by a force that rotates it around a longitudinal axis. The following paragraphs define the elements of transverse stability and provide a method to calculate the transverse stability characteristics of a vessel. 2-2.1 Height of the Center of Gravity (KG). One of the primary concerns in transverse stability is the height of thecenter of gravity above the keel. This distance is measured in feet. In most ships, the center of gravity lies between a point six-tenths of the depth above the keel and the main deck. The position of the center of gravity depends upon the position of weights in the ship and changes whenever weight is added, removed or shifted. To calculate the height of the center of gravity, the following stepsare necessary:
2-1

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a. Classify all the weights in the ship. b. Determine the height of each weight above the keel. c. Multiply each weight by the height above the keel to determine the moment of the weight. d. Total the weights and the moments of weight. e. Divide the total of the moments of weight by the total weight to determine the height of the center of gravity.EXAMPLE 2-1 CALCULATION OF THE HEIGHT OF THE CENTER OF GRAVITY (KG) A ship has the following weights on board: Material Ship’s structure Machinery Stores Fuel Cargo Weight (w) 2,000 500 400 250 800 Height above the keel (kg) 15 10 20 5 14

What is the height of the center of gravity? A tabular format is convenient for this type of calculation. Weight w 2,000 500 400 250 800 Sums 3,950
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Heightabove keel kg 15 10 20 5 14

Moment of Weight w x kg 30,000 5,000 8,000 1,250 11,200 55,450

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Height of the center of gravity: KG = sum of the moments of weight --------------------------------------------------------------------------total weight

55, 450 KG = ------------------3, 950 KG = 14.04 feet 2-2.2 Height of the Center of Buoyancy (KB). The height of the centerof buoyancy above the keel or baseline is another important distance in stability. This distance is measured in feet. Because the center of buoyancy is the geometric center of the underwater body of the ship, the height of the center of buoyancy depends upon the shape of the ship. In flat-bottomed full ships, such as carriers and tankers, the center of buoyancy is lower than in finer lined ships,...