Using of versine and sagitta calculations for log sawing optimization, part 1: Circular cross-section

Hizir Volkan Gorgun

doi:10.4067/s0718-221x2021000100453

Abstract

Log sawing can be defined as a problem with obtaining squares from a cylindrical shaped raw material, log. There are traditional sawing methods such as live, cant, quarter, etc. for sawmills. However, they cant generally obtain maximum yield due to log and lumber variables for each log. Therefore, many mathematical approaches and computer programs were improved for log sawing. In this study, suitability of two geometrical calculations, versine and sagitta, were tried for log sawing process. Logs were assumed having cylindrical shape and circular cross section. The estimation accuracy of calculations were tested for live and cant sawing methods with in a drawing software. The results showed that one of versine equations works almost as well as the real dimensions. It is suggested that the equation can be used inside of algorithms for log sawing optimization. However, the real log defects such as taper, irregular cross-section, curvature, etc. should be considered for more realistic yield and accuracy

Highlights

Log sawing can be defined as a problem with obtaining squares from a cylindrical shaped raw material
Many approaches were tried for log sawing optimization; BOF (Best Opening Face), dynamic and heuristic programming, machine vision algorithms, AUTOSAW, GSS-A, GRASP A, KORKUT, TOPSAW computer programs, etc., (Hallock and Lewis 1971, Hallock et al 1979, Faaland and Briggs 1984, Lewis 1985, Occeña and Tanchoco 1988, Todoroki 1990, Chang and Guddanti 1995, Occeña and Schmoldt 1995, Korkut 2004, Zheng et al 2007, Bhandarkar et al 2008, Lin and Wang 2012)
Aim of this study to find an equation with giving certain results to use in log sawing optimization calculations

Summary

Introduction

Log sawing can be defined as a problem with obtaining squares from a cylindrical shaped raw material. Calculations of two geometrical approach (versine and sagitta) were tried for using in log sawing optimization. The suggested approaches, which were described in detail at below, tried to find accurately the relationship between slab thickness and width with using the trigonometric relations in unit circle. If a slab width could be estimated, first sawn board for live sawing or cant height for cant sawing can be calculated.

Results

Conclusion