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2o8
HARBOUR ENGINEERING.
(II.) Case of the unballasted pontoon immersed to any fraction of its depth.
—The foregoing is a special case in which the pontoon floats with exactly one-
half of its bulk immersed.
From the principles enunciated, and by means of the methods which have
been deseribed, it is not difficult to determine the locus and draw the curve
of buoyancy for the general case in which the pontoon floats with any pro-
portion of its volume under water.
Let fig. 181 represent the conditions in question, the surface level of the
water, RT, not being coincident with JX, the horizontal axis of symmetry of
the pontoon.
In the initial position, the centre of buoyancy lies at the point B on the
pli
axis QK, which is such that BK=——=-—. Taking B as origin and a
horizontal line through B as axis of x, we have (as explained in the preceding
investigation) for all values of A between zero and D,
AL , A2
611 y 61)
giving, as the equation of the curve,
The parabola thus defined passes through the points Z and ¥ where
RZ = TY= D, and constitutes the locus of the centre of buoyancy within the
limits a and ß situated on the diagonals of the parallelogram ZHNY.
So long as the corner, H, of the pontoon remains under water the
immersed section is a quadrilatéral. When the point II lies on the surface
the water-line passes through the point ¥ and the immersed area becomes
triangular, remaining in that form until in course of continued revolution