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Added Masses of Two-Dimensional Forms by Conformal Mapping
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The Bieberbach method of mapping a plane section into a circle is found to converge too slowly for practical application when the number of terms of an assumed transformation series is increased. A modification of the procedure, in which, after a first mapping by the Bieberbach method into a nearly circular section, the latter is mapped into a much more nearly circular section by a second application of the method, is found to yield sufficiently accurate results. A FORTRAN program for computing mapping functions is presented. Motivation for this development is to make available a more accurate procedure than is presently used in ship-vibration calculations for obtaining the added masses of ship sections in horizontal or vertical vibration at a free surface.
The Society of Naval Architects and Marine Engineers
Title: Added Masses of Two-Dimensional Forms by Conformal Mapping
Description:
The Bieberbach method of mapping a plane section into a circle is found to converge too slowly for practical application when the number of terms of an assumed transformation series is increased.
A modification of the procedure, in which, after a first mapping by the Bieberbach method into a nearly circular section, the latter is mapped into a much more nearly circular section by a second application of the method, is found to yield sufficiently accurate results.
A FORTRAN program for computing mapping functions is presented.
Motivation for this development is to make available a more accurate procedure than is presently used in ship-vibration calculations for obtaining the added masses of ship sections in horizontal or vertical vibration at a free surface.
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