Calculating the Cross-Curves of Stability Using the Hand-Held Programmable Calculator and Printer

Abstract

This paper describes a three-part program the author has written for the Texas Instruments 59 Programmable Calculator and PC-100A Printer for calculating the cross-curves of stability for a vessel at inclinations of 15, 30, 45 and 60 deg from its offsets. The intended application of this program is in preliminary design studies. The program is based on the following assumptions, discussed in the "Basic Ideas" section of the paper: The intersection of the draft and inclined waterlines at each station can be treated as the origin (0) of an x-y coordinate system; the areas of the immersed and emerged wedges can be approximated by the sums of areas of triangles; the centroid of each of these triangles can be located by calculating the point of intersection of two of its medians; the areas of the two wedges can be made equal by moving the origin a certain direction and distance along the draft waterline; and the vessel's vertical center of gravity lies at the bottom of the keel. The three parts of the program are explained in the paper's "Program" section; they are Offset Encoding, Wedge Equalization and Moment Calculation, and Righting-Arm (GZ) Calculation. "Using the Program" discusses program restrictions and describes how the program is used to compute cross-curves. The "Conclusions" section of the paper describes the advantages to the program user: No wedge or layer corrections are required, the actual or assumed KG is taken into account when the GZ is calculated, program operation is semi-automatic, and no large-scale full-body is required. In addition, the author has included an improved version of his curves-of-form program as an Appendix.