Naval Architecture (Paperback)

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 edition. Excerpt: ...rolling can be calculated by equation (6), page 311, so that U-2At--7 (8) which give a method of determining At numerically. Now both the curve RS and the curve RiSi have the ordinate at 0m for an asymptote, and if wc draw an ordinate near0m, it will cut off nearly the same areas from the figures bounded by RS and /?, -. We may, therefore, consider that the area under RS exceeds the area under R, Si by the area RSSRi, which can be measured by aid of a planimeter or otherwise. We shall then have for the approximate value of /, t=ti+2RSSiRiti+2(A-Ai) (9) Influence of Form on Rolling.--All ships will have approximate isochronous rolling for small inclinations; in fact the deviation for ordinary forms and for moderate inclinations are insignificant, and 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 metacentre, 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 t=li-2(Ai-A); 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)...