Søgning i bogen
Den bedste måde at søge i bogen er ved at downloade PDF'en og søge i den.
Derved får du fremhævet ordene visuelt direkte på billedet af siden.
Digitaliseret bog
Bogens tekst er maskinlæst, så der kan være en del fejl og mangler.
PIERHEADS, QUAYS, AND LANDING-STAGES.
207
is cut off within the parabola, and bisect it at the point C. Draw CB2 parallel
to the axis QK, intersecting the curve at the point B2. Then B2 is the centre
of buoyancy for the water-line FS. From B2 draw B2M2 at right angles to
FS so as to cut the axis QK in M2. M2 is the metacentre under the same
conditions.
The proof of the foregoing construction lies in the facts that the tan-
gent at the extremity of a diameter of a parabola is parallel to the chords
which are bisected by that diameter, and that the tangent to the curve
of buoyancy at any point is parallel to the line of flotation corresponding
to that point as centre of buoyancy.
Thus far, we have only dealt with centres of buoyancy lying within the
section HON ; that is for water-lines rauging between GN and HP.
For water-lines between HP and NG, it is necessary to construct the
parabola GZH. This being done (fig. 180), the curve of buoyancy is defined
from ß to y, and the corresponding positions of the metacentre may be
determined as already explained. They will lie, however, not on the axis QK,
but on the axis RT, parallel to which the lines, from the water surface to the
curve, must be drawn.
It is interesting to consider the water-line HP. There are two parabolic
chords appertaining to the position, viz., Hy and aP. The middle point of
the former is a, and of the latter y. Both the line aß, drawn parallel to the
axis RT of the parabola GZH, and the line yß, drawn parallel to the axis QK
of the parabola GBjP, meet at the point ß, which is the limiting position of
the centre of buoyancy for both parabolas. The line /3M8, perpendicular
to HP, gives extreme positions for the metacentre on the respective axes:
the upper limit M8 on QK, and the lower limit M4 on RT. In fig. 180,
owing to the particular ratio of L to D, the point M8 coincides with the
point Q.
The curve of buoyancy for the remaining moiety of the pontoon is simply
a replica, upon the other side of the diagonal HP, of the curve aßy.
The parabolas GBjP and GZH have three point contact ; that is, the curves
not only touch one another, but cross when continued.