Abstract
In this paper, exact hydrostatic particulars equations for the centre of buoyancy curve and metacentric locus curve are given for rectangular cross section using quadratic functions. Those equations have not been given for the hyperbola range of the heel angles so far, and here it is done by using basic quadratic functions and their horizontally symmetric immersion shapes, with two new methods defined: 1. Rotation of basic cross section shapes, and 2. Hydrostatic cross section area complement method that uses homothety or scaling properties of emerged and immersed areas of the rectangular cross section. Observed metacentric curve for rectangle consists of semi-cubic parabolas and Lamé curve with 2/3 exponent and negative sign, resulting in the cusp discontinuities in the symmetry of those functions definition. In order to achieve above, two theorems are given: the theorem about scaling using hydrostatic cross section area complement and the theorem about parallelism of centre of buoyancy tangents with waterlines. After non-dimensional bounds are given for the existence of the swallowtail discontinuity of metacentric curve for rectangular cross section in the Part 1 of this paper, the proof of its position in the symmetry of rectangle vertex angle is given in this Part 2 of the paper, thus confirming its position from theory.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
