A Simple Method of Flooding Calculation

Abstract

Principal part of flooding calculation is divided into three parts. (1) To find the floodable volume so as to make the ship after flooding float at the trimmed water line which crosses the margin line only at one point, and the longitudinal position of its centre of volume. (2) With the given distribution of sectional area below that trimmed water line, to find the floodable length and the position of its middle point. (3) To find the end points of the floodable length curve. In this paper, the following methods are adopted to carry out these calculations.As an extension of the displacement calculation, at several parallel water lines between the load water line and deep water line, the volume above L.W.L. (v), the distance of its centre of volume from midship (λ), the distance of the centre of flotation. from midship, and the corresponding longitudinal metacentric radius (R) are calculated, and the profile between the L.W.L. and margin line with the locus of centre of flotation of even keel water line (I) (scale of depth being taken as ten times that of length), sectional area curve below margin line (II), and the plan area curve of margin line (III) are prepared.(1) Neglecting Leclert's correction, from the centre of flotation of an intermediate even keel water line between m.l. and L.W.L., two tangent lines (or lines through the end points of m.l.) are drawn towards fore part and aft part, and their inclinations α are measured.By virtue of the relationd=V0+v/vR tan α+λ (V0 : vol. below L.W.L.) the longitudinal distance d of the centre of floodable volume v from midship is calculated. (In this formula, d and α are assumed to be positive when referred to the fore part, λ being taken as positive for the centre of volume of layer v allocated after midship.) The draft de of corresponding even keel water line is also noted. With the base of d, curves of v (floodable volume curve) and of de (even keel draft curve) are drawn.(2) As for a certain value of d, the corresponding v and de are read and with (I), through the centre of flotation corresponding to de, a tangent line to margin line is drawn. Now, d being assumed to be the first approximation to the position of the middle point of the floodable length, the sectional area Am below margin line by (II), the height hm between margin line and the tangent by (I), and the breadth bm of the margin line plan area by (III) are taken at the position d, then the sectional area a0 below the trimmed water line at d will be given by a0=Am-bmhm, and the first approximate value of the floodable length 2l will be v/a0. By the same way, the sectional areas ae and am at d±l can be obtained. Assuming the distribution of sectional area below the trimmed water line as a parabola of second order nearly within this range, the exact values of the floodable length LF and the distance of its middle point from a0, section Ej can be given by 2lL and 2le, in which L and e are taken from the diagram of Fig. 4 with the given values of μe=ae/a0 and μm= am/a0.