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 TM 55-1905-223-SDC
e. Therefore, timing the roll is of little practical use in evaluating damaged stability. Knowledge of this
relation between period of roll and GM is useful in giving one the general feel of the ship's stability as it rolls.
A ship which has a logy roll has low GM; a stiff ship has high GM.
ANGLE OF LIST AT WHICH MAXIMUM RIGHTING ARM (GZ) OCCURS. General information
regarding angle at which maximum righting arm develops:
a. In FIGURE 5-2, the maximum value of the righting arm occurs at A, an angle of heel of about 39.
b. The angle at which the maximum righting arm develops is significant because it is the angle of
inclinatoin beyond which the ship cannot safely assume a permanent list, even under ideal conditions in calm
water.
DYNAMIC STABILITY . The work that must be done on a ship to heel it over is equal to the moment
with which the ship resists inclination (righting moment) times the angle through which this moment acts.
Hence, dynamic stability is equal to righting moments times angles of inclination. If the cause of the inclination
is removed, the dynamic stability becomes available as energy to return the ship to its upright position.
In a sense, this is similar to the work done in compressing a spring. When the pressure is removed,
the spring can do work as it expands, delivering back the energy used to compress it.
On the ship's curve of righting moments (FIGURE 5-4), the area between the curve and the base
represents the product of the moments (measured vertically) times the angles (measured horizontally)
through which the ship heels. Therefore, the area under the curve up to a given angle represents the
dynamic stability of the ship at that angle. That amount of work must be done on the ship to heel it, and that
amount of energy will become available to right the ship when the cause of the inclination is removed.
In FIGURE 5-4, the dynamic stability at 25 is represented by the shaded area. The unshaded area
under the curve is the reserve of dynamic stability; i.e., the work that must be done beyond 25 to continue
heeling the ship until it cap sizes.
5-4
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