Modeling the Cupping of Lumber

Philip H. Mitchell


Wood shrinks anisotropically as it loses hygroscopic moisture. While longitudinal shrinkage (parallel to the grain) is nearly negligible in normal wood, transverse shrinkage (across the grain) is significant and characterized as tangential and radial shrinkage. The application of average tangential shrinkage values to a rectangular cross section results in errors, especially for boards cut from near the center of the log. In addition, using a Cartesian coordinate system to calculate shrinkage cannot provide an estimate of cup. Calculating shrinkage and cup deformation using a previously developed model, this Excel model can provide a more realistic image of the final cross section and a more accurate estimate of shrinkage. The model is dependent on wood species, initial and final moisture contents, and location of the board within the log. This paper describes and illustrates uses of the model.


Lumber; Radial; Tangential; Shrinkage; Cup; Crown; Deformation; Differential shrinkage; Polar geometry; Dry kiln; Drying defect; Modeling; Excel

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Welcome to BioResources! This online, peer-reviewed journal is devoted to the science and engineering of biomaterials and chemicals from lignocellulosic sources for new end uses and new capabilities. The editors of BioResources would be very happy to assist you during the process of submitting or reviewing articles. Please note that logging in is required in order to submit or review articles. Martin A. Hubbe, (919) 513-3022,; Lucian A. Lucia, (919) 515-7707, URLs:; ISSN: 1930-2126