A Treatise On The Principles And Practice Of Harbour Engineering

2o6 HARBOUR ENGINEERING. buoyancy, it is only necessary to draw, perpendicular to the a line from the given point B2 on the buoyancy curve until it axis QK. Its position may be located algebraically, thus:— ' B1M2=M2C + CB1 = M2C + y. Now, the triangles CB2M2 and RFO are similar, their sides tively at right angles to one another. Therefore water surface, intersects the being respec- M2C =!g.CB2 L SA*’ and But BlM2=2^a:+y’ AL , A2 a:- and y = —-, 6D J 6D whence substituting 1.2 A2 1 2 12D 611 T 2 So when A is zero in the initial position, B^l^ ^^j and when A = RH, BjM2=—+—. 1 2 12D 6 Tire range of position of the inetacentre is accordingly within a length upon the axis QK, and, similarly, within a length ^ upon the axis RT. A much simpler method, however, may be devised for obtaining the position of the metacentre by geometrical construction. It will be observed that the equation of the parabola, 60 y L2 ’ is satisfied by the values «=—-, y=—; that is to say, the curve passes through the points G and P, which are the uppermost corners of the pontoon. Knowing also the vertex, Bp of the curve, it is a very easy matter to con- struct, by auy of the recognised methods, the parabolic arc GB^,* the portion of which, aß lying between the semi-diagonals HO and ON, constitutes a part of the buoyancy curve (fig. 180). Now, for any assigned water-line FS, take the chord fs on this line which * Vide construction, fig. 187, p. 213.