Naval architecture by Peabody Cecil Hobart 1855-1934

Author:Peabody, Cecil Hobart, 1855-1934
Language: eng
Format: epub
Tags: Naval architecture
Publisher: New York, J. Wiley & Sons; London, Chapman & Hall, limited
Published: 1904-03-25T05:00:00+00:00

for practical purposes it is sufficient to calculate the time of rolling by equation (6), p. 000, for any ship.

The graphical method just described allows us to determine from the metacentric curve of a given ship, or from the curve of statical stability, what the influence of form will be on unresisted rolling. Suppose that the metacentric curve for a given ship rises above the involute of a circle drawn from the centre of gravity through the meta-centrc, as shown by Fig. 143. Then for a given angle of inclination the righting moment is evidently greater than it would be for the supposititious ship with the involute for the metacentric curve. Then in a figure like 142 the curve OM will rise above the line OM», and consequently RS will lie below RiSi, so that equation (9) will take the form

that is, the actual ship will have a shorter time of rolling than the supposititious ship. The deeper the ship rolls the quicker it will roll. But a comparison of the equations

D(h-a) sin d and

D{r,-a)e

shows that the line OMi and the curve OM (in Fig. 142) very nearly

coincide for small angles, because h is nearly equal to r^ and sin 0

is nearly equal to 0. More exactly, the line OMi is the tangent to the curve OM at the origin. The conclusion is that when the curve of statical stability for a ship rises above the tangent to that curve at the origin, as represented by OMy Fig. 144, the ship will roll more quickly as it rolls deeper; on the contrary, the ship will roll slower as it rolls

more deeply if its curve of statical stability lies below the tangent at

the origin as shown by OM', Fig. 144.

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