ANGLE OF INCLINATION
,FIG. 13.—Curves of Stability of " Monarch " and " Captain."
the stability to. some extent. The effect of freeboard on the range and on the safety of ships is also illustrated by a comparison between the curves of stability (fig. 13) of the armoured turret ships " Monarch " and " Captain," the latter of which was lost at sea in 187o. These vessels were similar in construction and dimensions except that the freeboard of the " Monarch "was 14' 0" and that of the " Captain " 6' 6"; the smaller freeboard of the " Captain " was associated with a slightly lower position of the centre of gravity and a greater metacentric height. The stability curve of the ' Captain " in consequence rises rather more steeply than that of the " Monarch " up to about 14° when the deck edge is immersed ; the righting lever then rapidly. declines, and vanishes at 54a° in contrast to .the " Monarch's," where the maximum righting lever is doubled and range augmented 1.3 times by the additional freeboard. For the influence of the range in enabling a ship to withstand a suddenly applied force see " Dynamical Stability."
Again, for the boxshaped vessel previously considered, if the breadth is modified successively from 30 ft. to 35, 25 and 20 ft., other features remaining unaltered, the curves of stability then effect of obtained are represented by BB, CC and DD in fig. 12. It is beam.
seen that alteration in beam affects principally the stability
levers at moderate angles of inclination, while at 90° inclination the curves all intersect. Since at small angles GZ=GM.B (in circular
3.0 c25 =20
id
.~•'I i•/.[f4GEN .A1G HEI—GNT 2,
0• —` I 30° 45° 7'i •y 1
Angie of Inclination. :
`l N ?4.
of variation in height of centre of gravity.
measure) approximately, the initial slope of the curve is proportional to GM, and the tangent to this curve at the origin can be drawn by setting by the value of GM as an ordinate to an angle of one radian (57.3 ) as abscissa, and joining the point to the origin. (See figs. 10 and II.) The height of the metacentre above the centre of buoyancy will, caeleris paribus, vary with the cube of the breadth, and an increase of beam will result in a large increase of stability at moderate angles.
Finally the effect of an alteration in the vertical position of the centre of gravity is illustrated by the three stability curves of a steam yacht in fig. 14, where the centre of gravity is Effect of successively raised 1 ft. In the condition corresponding position of to the fourth and lowest curve, the GM is egative (—•2 ft.) c.a and so also are the righting levers up to 15° when the curve
crosses the axis; from 15 to about 52° the GZ is positive, but above
35
30
30
20
25
30
End of Article: ANGLE OF 

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